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| Meta Title | Cryptocurrency Price Prediction Using Sliding Empirical Mode Decomposition with Economic Variables: A Machine Learning Approach |
| Meta Description | The cryptocurrency market has attracted significant attention from global investors, with Cardano (ADA) ranking among the top cryptocurrencies by market capitalization. However, predicting ADA returns remains challenging due to the complex, multi-scale dynamics influenced by Federal Reserve policies, geopolitical events, and high-frequency trading. This study proposes a “Sliding EMD–Multi Variables” framework for cryptocurrency return prediction, leveraging Empirical Mode Decomposition’s multi-scale fractal properties to capture nonlinear dynamics at different time scales. The sliding window decomposition method addresses data leakage issues while incorporating key economic and policy variables at the component level. The empirical results demonstrate that the Sliding EMD system significantly outperforms univariate and multivariate benchmarks. Compared to the univariate system, it improves MSE, RMSE, SMAPE, and DSTAT by 0.83%, 0.42%, 5.23%, and 0.43%, respectively, while enhancing investment metrics (maximum drawdown, Sharpe ratio, Sortino ratio, Calmar ratio) by 0.19, 0.36, 0.95, and 0.15. Against the multivariate system, improvements reach 5.52%, 3.14%, 5.74%, and 17.62% in prediction accuracy, with investment performance gains of 0.47, 1.69, 4.27, and 0.31. Incorporating economic variables at the component level yields additional improvements of 0.94%, 0.47%, and 0.78% in MSE, RMSE, and MAE. These findings offer valuable insights for cryptocurrency portfolio optimization using fractal-based decomposition methods. |
| Meta Canonical | null |
| Boilerpipe Text | 1. Introduction
Cardano cryptocurrency (ADA) holds a significant position in the cryptocurrency market, ranking among the top ten globally with a market capitalization of around 26.17 billion USD. Its growing institutional recognition is underscored by major financial infrastructure developments, such as CME Group’s announced plan to launch ADA-linked futures contracts, reflecting its established liquidity and maturation within the digital asset ecosystem (
https://www.nasdaq.com/press-release/cme-group-expand-crypto-derivatives-suite-launch-cardano-chainlink-and-stellar
, accessed on 15 January 2026). Cardano utilizes the Ouroboros proof-of-stake consensus mechanism, which its founder estimates consumes less than 0.01% of the energy compared to the Bitcoin network (
https://www.the-independent.com/space/cardano-crypto-bitcoin-elon-musk-b1849021.html
, accessed on 18 May 2021). This energy efficiency has drawn the attention of investors focused on ESG (Environmental, Social, and Governance) criteria [
1
].
ADA’s price volatility is highly susceptible to shifts in macroeconomic conditions and broader financial environments. Elsayed et al. (2022) [
2
] found a synergistic effect between the macroeconomic environment and cryptocurrency trading volumes. Feng et al. (2025) [
3
] argued that changes in regulatory policies have increased the volatility of cryptocurrency prices. Aharon et al. (2021) [
4
] discovered a dynamic correlation between the US dollar exchange rate and cryptocurrency prices. There is also risk contagion between different cryptocurrencies [
5
]. Moreover, the connections between traditional financial markets and cryptocurrencies have become more frequent [
6
]. Consequently, incorporating such external determinants into forecasting models is crucial for improving prediction performance and understanding the multi-scale drivers of ADA prices.
The volatility of ADA prices and its impact on the economy and financial markets have attracted significant academic attention. ADA’s market value fluctuations affect the consumption sector through wealth effects and, via chain reactions, influence upstream and downstream companies in the blockchain industry [
7
]. This price instability increases the systemic risk premium in the cryptocurrency market, transferring risk to the traditional financial system through cross-market correlations. Notably, ADA’s price exhibits volatility clustering, long-range dependence, and multifractal characteristics across different time scales, reflecting the complex nonlinear dynamics inherent in cryptocurrency markets [
8
]. These multi-scale fractal properties challenge classical financial time series models that assume linear relationships and stationary processes. As a result, developing a stable and reliable prediction system that accounts for multi-scale dynamics is crucial for ADA.
Current cryptocurrency price prediction methods have evolved from traditional econometric models to machine learning techniques and “decomposition–ensemble” hybrid methods [
9
]. Econometric models face limitations in capturing non-linear features [
10
], while machine learning methods can excel in modeling complex patterns [
11
]. However, when dealing with multi-scale, nonlinear signal data like cryptocurrency returns, even single machine learning algorithms may not achieve ideal predictive performance without using hybrid models like “decomposition–ensemble” [
12
].
The “decomposition and ensemble” framework, rooted in multi-scale signal processing and fractal analysis, can decompose complex financial signals into multiple frequency components corresponding to different time scales. This multi-resolution approach aligns with the hierarchical structure of financial market dynamics, where short-term trading behavior and long-term macroeconomic trends operate at distinct temporal scales. Next, it applies ensemble-based recombination techniques to filter out extraneous noise. By forecasting each meaningful component separately and then summing those forecasts, this “divide-and-conquer” approach improves the accuracy of detecting complex multi-scale dynamics. However, decomposition methods applied to the full sample may result in information leakage, as the decomposition of historical data points can be influenced by the statistical properties of future data when the entire series is processed at once, thereby contaminating the training set with information that would not be available in a realistic sliding forecasting setting. Several scholars have explored algorithms like sliding VMD and sliding EEMD for financial asset price prediction [
13
]. However, research on applying sliding decomposition algorithms that preserve the temporal hierarchy to cryptocurrency return prediction is still limited. To address the information leakage issue inherent in full-sample decomposition, the sliding window approach processes data sequentially, ensuring that each training set uses only information available up to that point. This preserves the temporal hierarchy and prevents future information from contaminating the prediction process, making it a methodologically sound framework for cryptocurrency return forecasting. Additionally, incorporating essential factors, such as key policy and economic variables, at different frequency scales into sliding decomposition algorithms will enhance the understanding of the multi-scale drivers of ADA prices and assist cryptocurrency market investors in optimizing their portfolios.
To address the limitations mentioned above, this study focuses on the following questions: Does sliding decomposition that captures multi-scale dynamics improve the accuracy of ADA return predictions compared to traditional non-decomposed frameworks? Based on the existing literature, can incorporating key economic variables at the component level across different time scales into the prediction model enhance the forecasting performance for ADA? Which method, variable-driven or multi-scale sliding decomposition, leads to greater improvements in prediction? Can investment performance based on fractal-based sliding decomposition provide better results, helping investors make more informed decisions?
This research evaluates and compares four different forecasting frameworks: a Univariate Prediction System (System 1), a Multivariate Prediction System (System 2), the “Sliding EMD” prediction system (System 3), and the “Sliding EMD–Multi Variables” prediction system (System 4). Comparing System 2 with System 1 allows for testing whether incorporating influencing factors into the raw ADA series improves prediction accuracy. The comparison between System 3 and System 1 examines whether the Sliding EMD that captures multi-scale fractal properties can improve forecasting accuracy compared to a non-decomposed univariate system. The comparison between System 3 and System 2 demonstrates the relative advantages of multivariate and multi-scale decomposition approaches. Lastly, the comparison between System 4 and System 3 tests whether incorporating factors at the component level across different frequency scales in the “Sliding EMD” framework can further enhance prediction.
The innovation of this study lies in the following aspects: First, this study directly compares the “Sliding EMD” framework that exploits multi-scale temporal structures with traditional frameworks to evaluate the effectiveness of sliding decomposition technology in ADA prediction. To avoid the data leakage issue caused by applying traditional full-sample decomposition algorithms to ADA returns, this study uses the Sliding EMD method with a fixed window to predict ADA returns. Unlike existing studies that apply sliding decomposition, we employ unsupervised K-means clustering to adaptively group the derived components into high- and low-frequency clusters based on their intrinsic statistical properties. This clustering approach leverages the natural frequency separation inherent in EMD’s multi-scale decomposition, allowing us to capture both rapid market fluctuations and gradual trend movements. This approach not only integrates information from different frequency components to enhance prediction performance but also lays the foundation for further incorporating the impact of economic variables on different frequency scales.
Second, leveraging existing research on ADA’s influential factors, seven main categories of influencing variables are identified: macroeconomic variables, social variables, exchange rate variables, competitive variables, financial variables, commodity variables, and policy variables. Using Least Absolute Shrinkage and Selection Operator (LASSO) regression, significant variables influencing both the raw returns and decomposed components at different time scales are determined. The dynamic factor selection process using LASSO can be integrated into the Univariate Prediction System to form a Multivariate Prediction System. When incorporated into the “Sliding EMD” system, this results in the “Sliding EMD–Multi Variables” system that accounts for scale-dependent economic influences.
Finally, based on rigorous error metrics and statistical tests, this study yields three key insights that advance our understanding of ADA return forecasting. First, the multi-scale Sliding EMD framework exerts a stronger influence on prediction accuracy than dynamic factor selection via LASSO. Second, the prediction performance of the Sliding EMD system consistently surpasses that of the multivariate system. Third, the “Sliding EMD–Multi Variables” system delivers a slight improvement over the “Sliding EMD” system, further enhancing forecasting accuracy. This system integrates fractal-based decomposition with scale-specific economic variables, while the conventional multivariate approach proves comparatively ineffective. These findings collectively affirm that the predictability of ADA returns is fundamentally shaped by economic factors operating across distinct frequency components and time scales. To demonstrate the practical utility of these insights, we conduct an investment performance analysis, which confirms that the proposed framework aids investors in optimizing portfolio allocation, enhancing risk-adjusted returns, and mitigating downside risk, thereby offering actionable guidance for financial decision-making.
The structure of this paper is as follows:
Section 2
provides a literature review on the main drivers and prediction methods for ADA;
Section 3
details the four prediction frameworks employed in this study for ADA returns;
Section 4
analyzes ADA returns and key variables used in this study, with a discussion on the variables selected via LASSO;
Section 5
presents a comparison of the prediction results of the four frameworks for ADA returns, performance tests, and corresponding investment performance comparisons;
Section 6
discusses the research findings; and
Section 7
concludes the study with investment insights.
2. Literature Review
2.1. Key Drivers of ADA Price
As a prominent cryptocurrency, ADA exhibits significant return correlations with other major digital assets. This interdependence stems from shared market mechanisms and investor psychology. Specifically, price appreciation in large-capitalization cryptocurrencies such as Bitcoin and Ethereum, which is typically driven by institutional inflows, favorable regulatory developments, or broader macroeconomic tailwinds, tends to increase overall market risk appetite. This shift in sentiment encourages capital to flow across the cryptocurrency ecosystem, activating price transmission channels that subsequently elevate ADA’s valuation [
7
]. Moreover, ADA is primarily traded against Bitcoin (ADA/BTC) and stablecoins such as USDT (ADA/USDT). Consequently, pronounced fluctuations in Bitcoin often induce passive, correlation-driven adjustments in the ADA/BTC pair, while ADA/USDT valuations remain additionally exposed to shifts in overall market sentiment and liquidity conditions [
14
].
ADA’s price dynamics are significantly shaped by macroeconomic and policy variables, including exchange rates, economic uncertainty indices, and fiscal and monetary policies. Exchange-rate movements, particularly in the U.S. dollar, exert a notable pressure on cryptocurrency valuations: a strengthening dollar typically dampens investor appetite for risk assets, leading to downward pressure on ADA’s price [
4
]. Concurrently, heightened economic policy uncertainty elevates perceived risk within the cryptocurrency sector, which further suppresses ADA’s market performance [
2
]. Conversely, ADA may serve as an effective inflation-hedging instrument; rising inflation expectations often drive capital toward cryptocurrencies as stores of value, thereby boosting ADA’s price [
15
]. Moreover, accommodative fiscal and monetary policies stimulate liquidity and risk-taking sentiment, indirectly fostering bullish conditions in the cryptocurrency market and supporting ADA’s upward momentum [
16
].
The price of ADA is notably influenced by developments in both financial and commodity markets. In equity markets, fluctuations in stock prices can generate spillover effects on cryptocurrency valuations. As demonstrated by Attarzadeh et al. (2024) [
17
], a measurable transmission of volatility and returns from traditional equities to ADA exists, a linkage that typically reflects concurrent shifts in broader risk sentiment and liquidity conditions affecting both asset classes. Meanwhile, commodity markets exert influence through a more structural channel, since the operational costs of blockchain networks depend substantially on hardware components, including specialized metals used in mining hardware and energy consumption, whose prices are tied directly to commodity cycles. Rising costs in these inputs, as noted by Jiang et al. (2025) [
18
], can constrain network expansion and operational efficiency, thereby indirectly pressuring the valuation of cryptocurrencies such as ADA.
Online sentiment and extreme events constitute critical external drivers of ADA’s price dynamics. Investor attention, often proxied by search volumes on platforms such as Google, reflects real-time shifts in retail and speculative interest. As noted by Aslanidis et al. (2024) [
19
] and Hoang et al. (2024) [
20
], this attention can rapidly translate into trading pressure and price momentum for cryptocurrencies including ADA. Beyond mere attention metrics, broader sentiment extracted from social media and news coverage further amplifies short-term volatility, as herd behavior frequently characterizes cryptocurrency markets. Extreme events, including geopolitical conflicts, trade disputes, or large-scale natural disasters, introduce sudden uncertainty and risk-off sentiment across global markets, triggering pronounced fluctuations in cryptocurrency valuations. Moreover, regulatory and policy announcements, particularly from influential jurisdictions like the United States, directly shape market structure and investor confidence. Będowska et al. (2024) [
21
] highlight that the official stance of U.S. authorities toward digital assets can alter liquidity conditions, institutional participation, and long-term adoption prospects, thereby exerting a sustained influence on ADA’s market trajectory.
Time-scale decomposition is theoretically and empirically essential for cryptocurrency forecasting, as it aligns with the Heterogeneous Market Hypothesis (HMH). The HMH posits that market participants operate on distinct investment horizons, driving price formation at multiple frequencies. Low-frequency components predominantly reflect fundamental macroeconomic forces, which evolve slowly and anchor the intrinsic value of assets. In contrast, high-frequency components capture transient market microstructure noise, including speculative trading, liquidity shocks, and immediate reactions to exogenous events. By isolating these frequency bands, predictive models can disentangle the distinct economic mechanisms at play: macroeconomic fundamentals govern long-term trends, while short-term volatility is driven by information asymmetry and behavioral factors [
22
]. This separation not only enhances forecast accuracy by reducing noise interference but also provides critical insights into cryptocurrency market dynamics, such as the differential impact of financial factors (high-frequency) versus monetary and fiscal policies (low-frequency). Thus, frequency-aware modeling is not merely a technical refinement, but also a theoretically grounded necessity for robust cryptocurrency prediction.
The existing literature has identified numerous economic and financial factors affecting ADA returns, yet seldom integrates them dynamically into predictive models. This limits both explanatory power and forecast accuracy. Our study addresses this gap by implementing a factor-informed prediction architecture that combines sliding window decomposition with LASSO-based dynamic variable selection. This approach captures scale-dependent and time-varying effects of key drivers, enhances interpretability, and provides an actionable framework for improving prediction accuracy and supporting investment decisions.
2.2. Cryptocurrency Price Prediction Methods
Forecasting cryptocurrency asset prices can be clearly divided into three approaches: traditional econometric models, machine learning, and the “decomposition–ensemble” system [
23
]. Traditional econometric models mainly include ARIMA, GARCH family, and HAR family models [
24
]. However, these models have strict assumptions, such as the linearity and stationarity of time series. Although some econometric models have developed new methods applicable to nonlinear data, overall, econometric models still exhibit significant limitations when it comes to capturing the complex financial time series signals of cryptocurrencies.
Machine learning emerged in the context of big data and artificial intelligence, with traditional machine learning algorithms such as Support Vector Machines (SVMs), Random Forest (RF), and Gradient Boosting Decision Trees (GBDTs) being commonly used in financial asset price prediction [
25
]. Long Short-Term Memory (LSTM) networks and Convolutional Neural Networks (CNNs) are classic deep learning algorithms for cryptocurrency prediction [
26
]. Overall, both traditional machine learning and deep learning can effectively capture the nonlinear characteristics of time series. However, in the 24/7 cryptocurrency market, the complex, chaotic features still compel researchers to turn to the development of hybrid models.
While deep learning models such as LSTM and GRU can capture complex nonlinear patterns in cryptocurrency forecasting, they frequently exhibit prediction instability manifested through output oscillations and heightened sensitivity to initialization and hyperparameter configurations [
27
]. Though tree-based ensemble methods (Random Forest, Gradient Boosting Regressor, XGBoost, and so on) are comparatively less flexible in modeling highly intricate relationships, they deliver markedly more stable and reproducible predictions.
The “decomposition–ensemble” system effectively handles the complexity of financial time series and has shown promising results in previous studies. Standard decomposition algorithms include Empirical Mode Decomposition (EMD), Variational Mode Decomposition (VMD), and Wavelet Transform (WT) [
28
]. By decomposing complex time series into components of different frequencies, predicting each component separately, and then aggregating the results, the prediction accuracy for cryptocurrency prices can be significantly improved. However, the existing “decomposition–ensemble” systems decompose the entire financial data sample before splitting it into training and test sets, leading to potential data leakage, as the training set may already include information from the test set [
29
].
As a data preprocessing and feature extraction method, Empirical Mode Decomposition (EMD) still demonstrates its unique superiority in many complex time series prediction tasks. When combined with deep learning models such as LSTM, EMD not only enhances the interpretability of data but also optimizes the prediction accuracy of the model, especially in the fields of stock market prediction, seasonality, and chaotic time series analysis [
1
,
30
,
31
]. Compared to alternative decomposition methods such as VMD and Wavelet Transform, EMD is fully data-driven and requires no prior assumptions, making it particularly suitable for the adaptive, multi-scale analysis of non-stationary financial series. Its balance of interpretability, adaptability, and computational efficiency offers a distinct advantage in modeling complex cryptocurrency returns [
32
]. Therefore, EMD still has irreplaceable advantages in improving prediction performance and robustness, especially when dealing with complex systems.
Building on previous research, this study explores a key issue: whether a sliding decomposition prediction method that overcomes data leakage can outperform the univariate system in predicting ADA returns. Additionally, we use the dynamic LASSO method to examine whether incorporating time-varying economic and policy factors can further enhance the prediction accuracy of ADA returns. These two aspects have often been overlooked in previous studies but are worth investigating [
33
].
To address the limitations identified in prior research, this study introduces the following innovative improvements. First, to overcome the constraints of traditional econometric models in handling nonlinear and non-stationary series, as well as the inadequacy of machine learning methods in capturing the complex, chaotic nature of cryptocurrency markets, we adopt a decomposition–ensemble framework capable of adapting to multi-scale dynamics. Second, we propose a hybrid framework integrating sliding window EMD with machine learning. This approach eliminates the look-ahead bias inherent in full-sample decomposition, avoids the structural constraints of recurrent networks (e.g., LSTM, GRU) on non-stationary series, and leverages the robustness and efficiency of models to deliver superior forecasting performance. Finally, by embedding LASSO-based dynamic factor selection into the prediction of distinct frequency components, we enhance the economic interpretability and forecasting accuracy of the model, thereby achieving a substantive methodological advancement over existing frameworks.
3. Methodology
This section introduces the framework for the Univariate Prediction System, the Multivariate Prediction System, the “Sliding EMD” prediction system, and the “Sliding EMD–Multi Variables” prediction system. We employ a suite of established machine learning models for these forecasting tasks, including Linear Regression (LR), Support Vector Regression (SVR), Random Forest (RF), Gradient Boosting Regression (GBR), and Extreme Gradient Boosting (XGB). These models were selected for their proven efficacy and computational efficiency in financial forecasting. While deep learning architectures can capture complex patterns, they often demand substantial computational resources, are prone to overfitting and output instability in high-frequency financial data, and may not consistently outperform well-tuned traditional machine learning models in return prediction tasks. In contrast, the chosen ensemble and kernel-based methods provide a robust balance between predictive power, interpretability, and training efficiency, and have been widely validated in prior cryptocurrency and financial time series forecasting studies [
34
]. Additionally,
Appendix A.1
,
Appendix A.2
and
Appendix A.3
provides detailed descriptions of the error metrics for prediction comparisons and the performance metrics for investment evaluation.
3.1. Univariate Prediction System
The modeling process for the univariate system is shown in
Figure 1
. First, a fixed window is set, and the BIC criterion is used to select the optimal lag period. The ADA returns for the corresponding lag period are taken as the univariate input, and the future ADA returns are set as the target variable for fitting. For example, with a fixed window of 800 and an optimal lag period of 2, the training set inputs include data from periods 1 and 2, 2 and 3,…, 798 and 799, and the corresponding training set outputs are 3, 4,…, 800. The model is trained using these input–output pairs. For the test set, the ADA returns for periods 799 and 800 are used as input, and the trained model is used to predict the ADA returns for the 801st period.
Figure 1.
The modeling process of the Univariate Prediction System. Note:
Figure 1
,
Figure 2
,
Figure 3
and
Figure 4
present the methodological workflow of the proposed forecasting systems and were created by the authors.
Figure 1.
The modeling process of the Univariate Prediction System. Note:
Figure 1
,
Figure 2
,
Figure 3
and
Figure 4
present the methodological workflow of the proposed forecasting systems and were created by the authors.
Figure 2.
The modeling process of the Multivariate Prediction System.
Figure 2.
The modeling process of the Multivariate Prediction System.
Figure 3.
The modeling process of the “Sliding EMD” system.
Figure 3.
The modeling process of the “Sliding EMD” system.
Figure 4.
The modeling process of the “Sliding EMD–Multi Variables” system.
Figure 4.
The modeling process of the “Sliding EMD–Multi Variables” system.
Figure A1
,
Figure A2
,
Figure A3
and
Figure A4
display the optimal hyperparameters for XGB, SVR, GBR, and RF models over 1199 sliding windows. In the “Sklearn” framework, dynamic hyperparameter selection is performed via grid search for each 800-period window. The results show that, for SVR, the parameter “C” is mainly 0.1, with some instances at 10. For XGB, the “maximum_depth” is typically 3, with smaller portions at 5 and 7, while the “learning_rate” is mainly 0.01. For GBR, the “maximum_depth” is mostly 3, with some at 5 and 7, and the “learning_rate” is 0.01. For RF, the “min_samples_split” is distributed across [
3
,
5
,
7
], and the “maximum_depth” is mostly 3, with smaller portions at 5 and 7.
3.2. Multivariate Prediction System
The modeling process for the multivariate system is shown in
Figure 2
. The construction of this system is based on the univariate system, where relevant variables affecting ADA returns are selected for each sliding window. The LASSO method is used for feature selection from seven major categories of variables: macroeconomic variables, social variables, exchange rate variables, competitive variables, financial variables, commodity variables, and policy variables. The regularization parameter
λ
in LASSO is determined within each window via time series cross-validation, which preserves temporal ordering and selects the value that minimizes the one-step-ahead forecast error on the training segment. Variables with non-zero coefficients are retained, and variables with a LASSO coefficient of 0 are discarded. Then, the fixed window is moved forward by one step, and the LASSO selection is repeated for each window until the prediction is completed. The setting of the sliding window approach can help identify the time-varying characteristics of the impact of these seven variables on ADA returns. Furthermore, the LASSO selection results are incorporated as covariates into the prediction model, which improves prediction efficiency by integrating the economically significant variables, thereby improving prediction accuracy.
Figure A5
,
Figure A6
,
Figure A7
and
Figure A8
show the optimal hyperparameters for XGB, SVR, GBR, and RF models applied to the multivariate sliding window over 1199 windows.
3.3. “Sliding EMD” System
The modeling process for the “Sliding EMD” prediction system is shown in
Figure 3
. For an 800-day fixed window, ADA returns are decomposed using the EMD algorithm into multiple modal components. These components are then adaptively grouped into high-frequency and low-frequency clusters via K-means clustering, which operates on a feature vector comprising the sample entropy of each component. This unsupervised clustering naturally separates components with a higher sample entropy into the high-frequency group and those with a lower sample entropy into the low-frequency group, based on the intrinsic complexity of their temporal patterns. This two-scale separation is grounded in the multi-scale nature of financial markets: high-frequency components capture short-term noise and transient shocks, while low-frequency components reflect long-term trends and persistent economic forces [
35
]. Grouping components into these two distinct regimes allows the model to tailor predictive strategies to different temporal dynamics, thereby enhancing interpretability and forecast accuracy. The BIC criterion is applied to select the optimal lag periods for both components. Predictions for each component are summed to obtain the ADA returns for the 801st day. The window then slides forward, and the EMD and K-means reconstruction process is repeated until predictions are completed. The “Sliding EMD” system addresses data leakage issues seen in previous studies, and K-means clustering offers low computational cost with effective reconstruction results. The high-frequency and low-frequency components can also incorporate additional variables. For machine learning methods, optimal parameter tuning is required for both components. To ensure no future information is used, hyperparameter selection is performed independently within each rolling window: a grid search is conducted on the in-sample data of the current window using walk-forward validation, and the best-performing set is retained to forecast the next out-of-sample point. This process yields two sets of dynamic hyperparameters, one for the high-frequency and one for the low-frequency component, that adapt to local market patterns.
Figure A9
,
Figure A10
,
Figure A11
,
Figure A12
,
Figure A13
,
Figure A14
,
Figure A15
and
Figure A16
display these dynamically selected optimal hyperparameters for the XGB, SVR, GBR, and RF models applied to the high-frequency and low-frequency components.
3.4. “Sliding EMD–Multi Variables” System
Building on the “Sliding EMD” framework, the “Sliding EMD–Multi Variables” prediction system incorporates LASSO dynamic factor selection for the high-frequency and low-frequency components obtained from each fixed window decomposition. This allows for information gain at the frequency component level, as shown in
Figure 4
. After component decomposition, reconstruction, and BIC optimal lag selection within each window, LASSO factor selection is applied to identify economic factors influencing ADA returns. The selected factors and optimal lag periods for each component are then used to predict the future values of both frequency components.
For a fixed window of 800, the ADA returns from periods 1 to 800 are decomposed using EMD, and the high-frequency and low-frequency components are reconstructed using K-means. The lag periods for each component are used for fitting, followed by the LASSO selection of key variables with non-zero coefficients for prediction. The predicted values for both components on the 801st day are then summed to obtain the predicted ADA returns. The window is then moved forward by one step, and the process is repeated.
Figure A17
,
Figure A18
,
Figure A19
,
Figure A20
,
Figure A21
,
Figure A22
,
Figure A23
and
Figure A24
show the dynamic optimal hyperparameters for XGB, SVR, GBR, and RF models applied to these components.
4. Data Description
4.1. ADA Price and Returns
The ADA return data cover the period from 13 July 2019 to 31 December 2024. Data frequency is daily, and the total data size is 1999.This period includes significant events such as the U.S.–China trade war, fluctuations in commodity prices, the COVID-19 pandemic, and geopolitical conflicts, which provide support for validating the stability of the forecasting system proposed in this study. All subsequent return calculations are based on the logarithmic difference method, which is formulated as follows:
y
t
=
ln
P
t
/
P
t
−
1
(1)
Figure 5
shows the daily closing price and return series of ADA (data source:
https://cn.investing.com/crypto/cardano/historical-data
, accessed on 26 January 2026). Before 2021, ADA’s technological development was limited, and its price remained low. In September 2021, a significant upgrade introduced smart contract functionality, attracting investor attention. This coincided with a global cryptocurrency bull market, pushing ADA’s price to a peak of
$
3.10. In 2022, macroeconomic tightening and industry crises caused a 60% market cap reduction, leading ADA’s price to fall to
$
0.25 by year-end, a 92% drop from its peak. In 2023, ADA introduced new technology and partnerships, but U.S. regulatory scrutiny hindered price growth. By 2024, with the approval of cryptocurrency-related financial products (spot ETFs), market confidence returned, and ADA’s price slightly rebounded to
$
0.70.
Historical data show that ADA’s price is susceptible to technological upgrades and industry events. Its high volatility is driven by both technological potential and the inherent risk of the cryptocurrency market. The return series highlights frequent, large fluctuations, indicating a significant uncertainty in ADA’s daily returns. This volatility persists, reflecting the ongoing high risk.
4.2. Seven Key Factors Influencing ADA
This study identifies seven key factors: macroeconomic, financial, commodity, exchange rate, policy, attention, and competition variables. Based on Corbet et al. (2020) [
36
], macroeconomic variables include the U.S. federal funds rate, CPI, unemployment rate, and the global Economic Policy Uncertainty index. Financial variables, as suggested by Sánchez et al. (2024) [
37
], include the S&P 500, NASDAQ, and VIX indices. Commodity variables, such as metal and energy prices, affect ADA based on Manavi et al. (2020) [
38
], with the CRB index representing commodity market influence. Exchange rate fluctuations like USD/CNY and USD/EUR relate to cryptocurrency volatility, prompting a focus on the exchange rate’s role in predictions. According to Isah et al. (2019) [
39
], policy variables such as U.S. fiscal and monetary policy indices significantly impact ADA. Following Auer et al. (2022) [
40
], the Google search index for key ADA events is used as a measure of attention, with 42 key events tested using Granger causality and synthesized via the GDFM model. The competition variable considers Bitcoin and Ethereum, as De et al. (2023) [
41
] found a competitive relationship among major cryptocurrencies.
Figure 6
presents the four outcomes of the subsequent LASSO screening: the NASDAQ Composite Index, S&P 500 Index, US Monetary Policy Index, and US Fiscal Policy Index.
Exchange rates for USD/CNY, USD/EUR, the S&P 500, VIX, NASDAQ, federal funds rate, U.S. CPI, and U.S. unemployment data are sourced from the Federal Reserve Economic Data (FRED) website:
https://fred.stlouisfed.org/
, accessed on 26 January 2026. CRB, Bitcoin, and Ethereum data come from the Choice Financial Terminal. The global EPU index, U.S. fiscal policy index, and U.S. monetary policy index are directly downloaded from
https://www.policyuncertainty.com/
, accessed on 26 January 2026.
To ensure temporal consistency and prevent the use of future information, all lower-frequency variables are manually aligned with the daily ADA return series. Specifically, for a given month, the same monthly value is assigned to every trading day within that month. This alignment preserves the chronological order of information and eliminates look-ahead bias, as only data available up to each prediction point are used in the rolling window forecasting process.
4.3. Factor Selection Results Based on Least Absolute Shrinkage and Selection Operator (LASSO)
4.3.1. Factors in the Multivariate Prediction System
In the multivariate sliding window prediction system described in the methodology section, the LASSO method dynamically selects factors from the seven key variables within each sliding window. Since this system performs less effectively than the “Sliding EMD–Multi Variables” prediction system, only a brief introduction to the factor selection results is provided.
Figure A25
shows the LASSO dynamic factor selection results. It reveals that, without decomposition, the NASDAQ index is selected in nearly all windows, highlighting its substantial impact on ADA returns. The S&P 500 is chosen in all windows until June 2023, indicating its comparable predictive importance. The U.S. monetary policy variable mainly contributes between October 2021 and May 2022, and in November 2024.
Figure A26
,
Figure A27
and
Figure A28
show the dynamic coefficient plots of the LASSO-selected variables for each window in the multivariate system.
4.3.2. Factors in the “Sliding EMD–Multi Variables” Prediction System
Figure 7
shows the LASSO dynamic factor selection results for the high-frequency components in the “Sliding EMD–Multi Variables” prediction system. Under the sliding window decomposition, the NASDAQ variable is selected in every window, and the S&P 500 is frequently selected until June 2023. U.S. monetary policy impacts the high-frequency component, especially before April 2022 and after November 2024, consistent with the multivariate sliding window results. U.S. fiscal policy affects the high-frequency component intermittently in 2021 and 2022. The coefficients for the NASDAQ and S&P 500 are inversely related: NASDAQ has a positive impact, while the S&P 500 has a negative one. Fiscal and monetary policy variables mainly have a negative impact, except for monetary policy in 2024, which has a positive effect.
Figure 8
shows the dynamic coefficient plots for the high-frequency factors in the “Sliding EMD–Multi Variables” prediction system. From September 2021 to January 2022, the NASDAQ coefficient is positively correlated with ADA, as the Federal Reserve reduced bond purchases, causing volatility in NASDAQ stocks and increasing the short-term correlation with ADA. During the same period, the S&P 500 coefficient fluctuates negatively, indicating a weakening correlation with ADA due to concerns about economic recession and a shift away from traditional industries. Monetary policy coefficients show a negative relationship with ADA, reflecting the impact of expected interest rate hikes, which led funds to flow into the U.S. dollar and Treasury bonds.
From May 2022, the NASDAQ coefficient turned negative, while the S&P 500 coefficient shifted positive, reflecting a decline in technology stock valuations and a rise in traditional industries, which led to a drop in ADA’s price. From January to May 2023, both coefficients are significantly negative due to the Silicon Valley Bank incident, which heightened concerns about financial stability. After May 2023, the NASDAQ coefficient turns slightly positive, reflecting a shift in U.S. Federal Reserve policy and easing expectations, driving both the Nasdaq index and ADA higher. In the second half of 2024, the monetary policy coefficient turns positive as the Federal Reserve signals interest rate cuts due to declining inflation expectations, prompting capital inflows into the cryptocurrency market.
The high-frequency model captures short-term shocks to the ADA market. As a barometer for tech stocks, NASDAQ’s volatility reflects market risk appetite and liquidity expectations, making ADA returns highly sensitive to tech sector sentiment. The S&P 500’s short-term fluctuations mirror macroeconomic risks and industry volatility, acting as a haven during systemic risk and returning to a risk asset status during liquidity expansion. The persistent negative fiscal policy coefficient reflects the impact of short-term fiscal funds and regulatory risks on ADA, while the dynamic monetary policy coefficient captures shifts in short-term liquidity cycles from tightening to easing.
Figure 9
shows the LASSO dynamic factor selection results for the low-frequency components in the “Sliding EMD–Multi Variables” prediction system. The NASDAQ variable is selected throughout, and the S&P 500 is frequently selected until June 2023, consistent with the high-frequency results. The factors for the low-frequency components align with those for high-frequency components, with NASDAQ having a positive impact and the S&P 500 having a negative impact.
Figure 10
shows the dynamic coefficient plots for the low-frequency factors in the “Sliding EMD–Multi Variables” prediction system. From September 2021 to January 2022, the NASDAQ coefficient was significantly positive and linked to the ADA contract technology upgrade. In May 2022, it briefly dropped due to a reduced correlation between tech stocks and cryptocurrencies from interest rate hikes. From September 2022 to early 2023, the coefficient continues to decline. After 2023, the NASDAQ coefficient becomes persistently positive but with a smaller magnitude, indicating a weakening long-term correlation with traditional markets.
The impact of the S&P 500 on the low-frequency component of ADA returns is more pronounced. From 2021 to 2023, the S&P 500 coefficient remains significant and negative, but after 2023 it becomes zero, indicating no further impact on ADA returns. As a diversified market index, the S&P 500 reflects a long-term driving factor that differs from ADA, with the coefficient showing a negative correlation between traditional industries and ADA.
The low-frequency model captures long-term market linkages, with policy shocks transmitted through market indices rather than policy variables. The common trend between U.S. tech stocks and ADA remains stable across cycles. The low-frequency data highlights ADA’s independence from traditional indices, filtering out short-term fluctuations and emphasizing the role of technology and macro events on the NASDAQ coefficient. The negative S&P 500 coefficient reflects the disconnect between the traditional economy and the cryptocurrency market, showing no correlation or a negative one with traditional economic cycles.
After sliding window decomposition, financial variables have the most significant influence. Policy variables impact high-frequency components but not low-frequency components. Compared to the non-decomposed system, fiscal policy significantly affects ADA after EMD. The high-frequency model focuses on short-term dynamics, while the low-frequency model captures long-term trends in market indices. These variable selections reflect the heterogeneous driving factors across time scales.
5. Empirical Results
This section consists of prediction results, investment results, MCS (Model Confidence Set) tests, and comparisons between the univariate system (System 1), multivariate system (System 2), “Sliding EMD” system (System 3), and “Sliding EMD–Multi Variables” system (System 4). The prediction metrics used include MSE, RMSE, MAE, SMAPE, and DSTAT, which represent the performance of different prediction system models. When predicting ADA returns, it is crucial to emphasize practical applicability, especially the impact on investment decisions. For investment results, metrics such as the average daily returns, maximum drawdown, Sharpe ratio, Sortino ratio, and Calmar ratio are used to evaluate the investment performance changes across different systems. Finally, to comprehensively assess the overall effectiveness of the prediction systems, the MCS test is more appropriate. Therefore, the MCS test is used further to verify the advantages and disadvantages of the four systems.
Table A1
provides the Univariate Prediction System prediction results,
Section 5.1
presents the forecasting results and investment performance of the Multivariate Prediction System,
Section 5.2
presents the “Sliding EMD” system prediction results and investment comparison, and
Section 5.3
presents the “Sliding EMD–Multi Variables” system prediction results and investment comparison.
5.1. Prediction Results for the Multivariate Prediction System
In the Multivariate Prediction System, the LASSO method is applied to the raw ADA returns series to select dynamic factors with non-zero coefficients for prediction.
Table 1
shows the prediction results for the five models under the multivariate, and
Table 2
presents the comparison between the Multivariate Prediction System and the Univariate Prediction System. The values in
Table 2
represent changes relative to the Univariate Prediction System, where a “–” indicates worse forecast performance and a “+” indicates better forecast performance. It can be seen that, aside from four error metrics in the GBR and XGB models where the Multivariate Prediction System performs better, all other model performances are worse. On average, the five models in the Multivariate Prediction System have worsened by 5.422%, 2.614%, 2.972%, 0.572%, and 13.226% in terms of MSE, RMSE, MAE, SMAPE, and DSTAT, respectively. Therefore, under the Multivariate Prediction System, when decomposition techniques are not used, the performance and investment efficiency after incorporating predictive variables are inferior to those of the Univariate Prediction System. The MCS test results in
Table A2
also indicate that the Multivariate Prediction System performs worse.
5.2. Prediction Results for the “Sliding EMD” System
In the “Sliding EMD” prediction system, a sliding window EMD, K-means clustering, and five prediction methods are applied, focusing on the multi-scale modal features of ADA returns data.
Table 3
shows the prediction results for the five models under the “Sliding EMD” System. The MSE, RMSE, MAE, SMAPE, and DSTAT for the LR model are 3.53 × 10
−4
, 0.0188, 0.0134, 1.64, and 0.510, respectively.
Figure 11
shows the comparison of this system with the Univariate Prediction System. The closer the comparison index of the radar chart is to the external circle, the better the improvement of the system will be. Assuming the prediction models remain unchanged, except for LR (MAE), XGB (MAE), GBR (MAE), and RF (DSTAT), the error metrics improve due to the sliding window decomposition technique. For instance, compared to System 1, the LR model improved MSE by 0.16%, RMSE by 0.08%, MAE by 0.42%, and SMAPE by 4.65%, and DSTAT remained unchanged. On average, the system improved by 0.828% for MSE, 0.416% for RMSE, 5.234% for SMAPE, and 0.418% for DSTAT.
Figure 12
compares the “Sliding EMD” system with the Multivariate Prediction System. Assuming the prediction models remain unchanged, except for XGB (MAE) and GBR (MSE, MAE), the decomposition technique in this system outperforms the Multivariate Prediction System for all other error metrics. For example, compared to System 2, the LR model improved MSE by 12.77%, RMSE by 6.60%, MAE by 7.23%, SMAPE by 5.62%, and DSTAT by 33.81%. On average, the five models improved by 5.522% for MSE, 3.144% for RMSE, 2.602% for MAE, 5.746% for SMAPE, and 17.616% for DSTAT.
Figure 12.
Comparison of prediction accuracy between the “Sliding EMD” system and the Multivariate Prediction System. Note:
Figure 11
,
Figure 12
,
Figure 13
and
Figure 14
are plotted by the authors based on the empirical results of this study.
Figure 12.
Comparison of prediction accuracy between the “Sliding EMD” system and the Multivariate Prediction System. Note:
Figure 11
,
Figure 12
,
Figure 13
and
Figure 14
are plotted by the authors based on the empirical results of this study.
Figure 13.
Comparison of prediction accuracy between the “Sliding EMD–Multi Variables” system and the “Sliding EMD” system. Note: The radar chart also shows percentage data. The closer to the center of the origin, the smaller the data becomes. The further out the data, the greater the percentage, and the stronger the improvement percentage in the comparison between the two systems.
Figure 13.
Comparison of prediction accuracy between the “Sliding EMD–Multi Variables” system and the “Sliding EMD” system. Note: The radar chart also shows percentage data. The closer to the center of the origin, the smaller the data becomes. The further out the data, the greater the percentage, and the stronger the improvement percentage in the comparison between the two systems.
Figure 14.
Daily return comparison for the “Sliding EMD–Multi Variables” system.
Figure 14.
Daily return comparison for the “Sliding EMD–Multi Variables” system.
The MCS test in
Table 4
shows that, when comparing System 3 with System 1, the univariate SVR is the worst, while the LR model in the “Sliding EMD” system performs the best. System 3 has an average ranking of 4.2, compared to 6.8 for System 1. When comparing System 3 with System 2, the SVR model under the Multivariate Prediction System performs the worst, and the GBR model under the Multivariate Prediction System performs the best. System 3 has an average ranking of 4.6, while System 2 has an average ranking of 6.2. Overall, System 3 outperforms both System 1 and System 2, which is consistent with the error metric results. The pure decomposition system outperforms both the non-decomposed and multivariate added prediction systems, proving the full effectiveness of decomposition techniques in ADA prediction.
Additionally, this study compares investment performance across the “Sliding EMD” system, the Multivariate Prediction System, and the Univariate Prediction System.
Table 5
presents the daily return comparisons. Compared with System 1, System 3’s models show the following improvements in daily return: LR by 9.00 × 10
−5
, GBR by 3.63 × 10
−4
, RF by 5.74 × 10
−4
, SVR by 2.50 × 10
−4
, and XGB by 5.43 × 10
−4
. Compared with System 2, System 3’s models improve by 2.64 × 10
−3
(LR), 3.76 × 10
−4
(GBR), 1.35 × 10
−3
(RF), 2.27 × 10
−3
(SVR), and 4.24 × 10
−4
(XGB). Overall, System 3 outperforms System 1 by an average of 3.64 × 10
−4
and System 2 by an average of 1.412 × 10
−3
in daily returns.
Table A3
,
Table A4
,
Table A5
and
Table A6
illustrate comparisons of the maximum drawdown ratio, Sharpe ratio, Sortino ratio, and Calmar ratio.
5.3. Prediction Results for the “Sliding EMD–Multi Variables” System
In the “Sliding EMD–Multi Variables” prediction system, this study builds upon the “Sliding EMD” system’s decomposition and reconstruction framework. For each fixed window, the high-frequency and low-frequency components obtained through reconstruction are combined with the non-zero coefficient factors selected by the LASSO model as covariates to assist in prediction.
Table 6
shows the prediction results for the five models under this system.
Figure 13
compares the results with System 3. For the LR model, the MSE improves by 0.94%, RMSE improves by 0.47%, MAE improves by 0.78%, SMAPE worsens by 2.62%, and DSTAT worsens by 0.73%. In the MSE metric, all models perform better, with an average improvement of 0.687%. The RMSE metric also improves on average by 0.338%. The MAE metric is seen as a disadvantage in GBR and XGB, but the other models show an average improvement of 0.266%. The SMAPE and DSTAT metrics do not surpass System 3. The above analysis indicates that incorporating economic variables into the frequency components in the “Sliding EMD–Multi Variables” system improves ADA return forecasting accuracy compared to the “Sliding EMD” system, albeit by a small margin.
Figure A29
shows the comparison with the Multivariate Prediction System. For the LR model, MSE improves by 13.59%, RMSE improves by 7.04%, MAE improves by 7.95%, SMAPE improves by 3.15%, and DSTAT improves by 32.82%. Decomposition technology brings significant improvements to all metrics, with the exception of GBR, which sees a slight decline. On average, the five models show improvements of 6.136% for MSE, 3.174% for RMSE, 2.844% for MAE, 3.154% for SMAPE, and 17.528% for DSTAT.
Figure A30
compares the ADA return prediction with the Univariate Prediction System. For the LR model, MSE improves by 1.10%, RMSE improves by 0.55%, MAE improves by 0.36%, SMAPE improves by 2.03%, and DSTAT worsens by 14.06%. Decomposition and multivariate inclusion lead to a slight deterioration in DSTAT, GBR (MAE), SVR (SMAPE), and XGB (MAE), while other models show improvements in MSE, RMSE, MAE, and SMAPE, with average improvements of 1.506% for MSE, 0.754% for RMSE, 0.13% for MAE, and 2.478% for SMAPE.
The MCS test results for System 4 are shown in
Table 7
. When comparing System 4 with System 1, the SVR model in the univariate system performs the worst, while the LR model in the “Sliding EMD” system performs the best. System 4 has an average ranking of 7, compared to 4 for System 1. When comparing System 4 with System 2, the SVR model in the multivariate system performs the worst, and the LR model performs the best. System 4 has an average ranking of 4.4, while System 2 has an average ranking of 6.6. When comparing System 4 with System 3, the SVR model under the “Sliding EMD” framework performs the worst, and the LR model under the “Sliding EMD–Multi Variables” framework performs the best. System 4 has an average ranking of 5.4, while System 3 has an average ranking of 5.6.
In the investment performance comparison for System 4,
Figure 14
shows the daily return metrics. Compared to System 1, except for the LR model, all models in System 4 perform better. The LR model worsens by 2.55 × 10
−4
, while GBR improves by 1.74 × 10
−4
, RF improves by 6.32 × 10
−4
, SVR improves by 4.14 × 10
−4
, and XGB improves by 2.86 × 10
−4
, with an average improvement of 2.502 × 10
−4
. System 4 performs better than System 2 across all five models, with LR improving by 2.29 × 10
−3
, GBR improving by 1.87 × 10
−4
, RF improving by 1.41 × 10
−3
, SVR improving by 2.44 × 10
−3
, and XGB improving by 1.67 × 10
−4
, with an average improvement of 1.2988 × 10
−3
. However, System 4 lags behind System 3, with only RF and SVR improving by 5.80 × 10
−5
and 1.64 × 10
−4
, respectively, resulting in an average decrease of 1.138 × 10
−4
.
Table A7
,
Table A8
,
Table A9
and
Table A10
present the comparisons for the maximum drawdown ratio, Sharpe ratio, Sortino ratio, and Calmar ratio. In terms of the maximum drawdown ratio, System 4 improves by an average of 0.166 compared to System 1, and by an average of 0.439 compared to System 2. For the Sharpe ratio, System 4 improves by an average of 0.114 compared to System 1, and by an average of 1.549 compared to System 2. The Sortino ratio shows an improvement of 0.560 for System 4 compared to System 1, and 3.876 compared to System 2. In the Calmar ratio, System 4 improves by an average of 0.0802 compared to System 1, and by 0.239 compared to System 2.
Based on the overall prediction results, investment outcomes, and MCS tests, the Multivariate Prediction System is inferior to the univariate system, the “Sliding EMD” system outperforms both the Univariate and Multivariate Prediction Systems, and the “Sliding EMD–Multi Variables” system does not show a significant improvement over the “Sliding EMD” system but significantly outperforms both the multivariate and univariate systems.
The advantage of the “Sliding EMD” system highlights the importance of the multi-scale composite system method combining the sliding window EMD and K-means clustering proposed in this study. EMD decomposes the complex ADA return series into components at multiple scales via multi-scale analysis, while the sliding window approach effectively prevents the data leakage inherent in traditional decomposition algorithms and ensures that each prediction step is based on real-time information. K-means clustering then adaptively reorganizes these components within each fixed window into high-frequency and low-frequency elements, enhancing prediction accuracy and enabling the subsequent inclusion of variable effects. System 3 significantly outperforms both the univariate and multivariate systems in prediction accuracy and investment performance, demonstrating that the combination of EMD and K-means clustering can effectively extract insights from the ADA time series and provide more reliable support for investment decisions.
Section 4.3.2
identified that U.S. stock market, U.S. fiscal policy, and U.S. monetary policy significantly affect different frequency components of ADA returns. The empirical results also show that the “Sliding EMD–Multi Variables” system delivers a slight improvement in forecasting accuracy compared to the “Sliding EMD” system, demonstrating the impact of these key economic variables.
6. Discussion of ADA Return Prediction Results
In recent years, many studies have combined machine learning with the multi-factor prediction of financial asset prices. However, current studies using decomposition algorithms have data leakage problems, and few use real investment performance to verify the model’s application value.
Table 8
compares these studies regarding sliding windows, variables, models, etc.
This section compares the “Sliding EMD–Multi Variables” framework with existing forecasting methods. A key question is whether the sliding window decomposition is better than the traditional univariate decomposition. Xu and Niu (2023) [
13
] found that the multi-step sliding window decomposition has a greater prediction advantage for oil price forecasting than the single-step one. However, the sliding decomposition is still not better than the traditional univariate forecast. Although the sliding window method can prevent data leakage, it also reduces the forecast accuracy. However, these studies rarely apply sliding window decomposition to ADA returns. Our results based on error indicators and MCS tests show that the “Sliding EMD” framework outperforms the traditional Univariate Prediction System in ADA return forecasting. Our research offers practical insights into whether including economic and financial variables improves ADA prediction and elucidates whether decomposition techniques and factor selection can further enhance forecasting accuracy.
The existing decomposition forecasting studies, such as those by Viéitez et al. (2024) [
29
], Buse et al. (2025) [
43
], and Li et al. (2022) [
28
], mainly focus on applying advanced single machine learning algorithms or combined models to different decomposed components to obtain comparative advantages but ignore the impact of combining important economic and financial variables, that is, enhancing forecasts through data-driven approaches. However, studies by Bouri et al. (2021) [
7
], Jiang et al. (2021) [
15
], and Hajek et al. (2023) [
42
] show that macroeconomic indicators, exchange rates, financial markets, commodities, monetary and fiscal policies, and online attention all significantly affect ADA returns. Including these variables can improve forecast accuracy, but few studies do so. In this study, based on the “Sliding EMD” framework, we use the LASSO method to screen factors that affect different frequency domain components of ADA returns within each fixed window and then incorporate these selected factors into the forecasting process. Compared with the “Sliding EMD” system, the “Sliding EMD–Multi Variables” system, which is constructed this way, further reduces the forecast error index. It improves investment performance through a data-driven approach and demonstrates the effectiveness of adding component-level variable effects in a sliding window decomposition framework. To date, ADA return forecasting studies have rarely examined the impact of economic and financial factors, especially within a sliding window decomposition framework. By doing so, our study provides practical insights into whether including economic and financial variables improves ADA forecasts and sheds light on whether decomposition techniques and factor selection can improve forecast accuracy.
Finally, these findings have significant practical value for policymakers, financial institutions, and investors. Policymakers can use the multi-scale composite framework developed in this paper as a macroprudential tool for the cryptocurrency market. For example, among the high-frequency components, US fiscal policy, US monetary policy, NASDAQ index, and S&P 500 index, all affect ADA returns. Regulators can establish a real-time monitoring system to monitor changes in these economic variables to prevent excessive volatility in ADA prices. For investors, using the “Sliding EMD–Multi Variables” forecasting system can increase daily returns by 3.64 × 10
−4
compared to the traditional Univariate Prediction System.
7. Conclusions
The Sliding EMD method and economic variables are critical in predicting ADA coin returns. This study constructs four prediction frameworks to assess their effectiveness: the traditional Univariate Prediction System (System 1), the Multivariate Prediction System (System 2), the “Sliding EMD” prediction system (System 3), and the “Sliding EMD–Multi Variables” prediction system (System 4). The empirical results indicate the following:
(1) Regarding the interpretability of ADA return forecasting, financial and policy variables significantly impact both the original ADA return series and the frequency components extracted through Sliding EMD, exhibiting time-varying effects. U.S. fiscal and monetary policies only affect the high-frequency components, while financial variables such as the S&P 500 and Nasdaq are significant drivers of both high- and low-frequency ADA returns.
(2) In terms of prediction performance, the constructed Multivariate Prediction System does not improve prediction performance. The “Sliding EMD “ prediction system and the “Sliding EMD–Multi Variables” prediction system frameworks demonstrate improvements over the traditional Univariate Prediction System. Specifically, System 3 improved MSE by 0.16%, RMSE by 0.08%, and SMAPE by 4.65%, with DSTAT being unchanged. System 4 follows closely, with improvements of 1.1% in MSE, 0.55% in RMSE, 0.36% in MAE, and 2.03% in SMAPE. These results indicate that Sliding EMD, combined with economic and financial driving variables at the component level, enhances the prediction of ADA returns.
(3) Based on the comparison of investment performance based on the prediction results, the daily return rate of System 3 is better than that of System 1. Similarly, the daily return rate of System 4 is also better than that of System 1. On average, the daily return rate of System 3 is 3.64 × 10
−4
higher than that of System 1; the daily return rate of System 4 is 2.502 × 10
−4
higher than that of System 1. These investment results are consistent with the prediction accuracy ranking, highlighting this study’s practical value.
This study innovatively applies sliding Empirical Mode Decomposition to predicting ADA returns. This method can decompose the original price series into intrinsic mode functions of different frequencies, effectively capturing information about different frequencies. At the same time, by correlating key economic and financial variables with varying components of frequency obtained using Sliding EMD, this study revealed for the first time that the impact of economic variables on ADA returns has a significant frequency dependence, and these impacts show time-varying characteristics. This provides a new perspective for understanding the complex driving mechanism of the cryptocurrency market.
The findings of this study have important practical significance and broad application prospects, especially for investors and traders, fund managers and quantitative teams, policymakers, and regulators in the cryptocurrency market. For investors and traders, the “Sliding EMD–Multi Variables” forecasting framework (System 4) provided by the study can be used as a core tool for building more accurate trading strategies. Its significantly improved forecasting accuracy directly translates into potential excess returns, which is of great value to active investors. For fund managers and quantitative teams, the study provides a ready-made forecasting tool (System 4), which reveals the frequency decomposition characteristics of the Cardano yield and its correlation mechanism with the macroeconomy. This provides a theoretical and empirical basis for fund managers to design quantitative strategies and conduct risk management. The improved forecasting accuracy directly translates into potential excess returns. This improvement is of great value to active investors. For policymakers and regulators, the study quantifies the significant impact of macroeconomic policies, especially U.S. fiscal and monetary policies, on the volatility of ADA returns from a short-term perspective. This helps policymakers provide decision-making references for formulating macroprudential regulatory frameworks and risk warning mechanisms.
Despite the current research’s findings, there are limitations and room for improvement in ADA return prediction. The K-means clustering method only divides the components into high-frequency and low-frequency categories. Clustering into more components may yield better results. As the research conclusions show, the machine learning models used in this study demonstrate a varying superiority across different prediction systems, and future research could explore using model averaging and weighted integration to combine the advantages of various models. This study examined the EMD algorithm but did not further test the effectiveness of other algorithms. Future research could explore decomposition algorithms with fixed component numbers (such as VMD and SSA), which remain potential areas for further study. Furthermore, the present framework was validated solely on ADA. Although ADA is a prominent and representative cryptocurrency, future work should extend the analysis to other major digital assets to assess the model’s generalizability across different market structures and volatility regimes.
Author Contributions
W.Z.: Conceptualization, Formal analysis, Investigation; Z.T.: Formal analysis, Writing—original draft, Investigation; X.Z.: Formal analysis, Writing—original draft, Investigation; Y.C.: Data curation, Software, Writing—review and editing; B.D.: Software, Visualization, Validation. All authors have read and agreed to the published version of the manuscript.
Funding
This research work was supported by the National Natural Science Foundation of China under Grant No. 72341030.
Data Availability Statement
The original contributions presented in this study are included in the article and
Appendix A
. Further inquiries can be directed to the corresponding author.
Conflicts of Interest
The authors declare no conflicts of interest.
Appendix A
Appendix A.1. Investment Strategy Design
The prediction results from the four systems discussed in the main text can be applied to the design of quantitative investment strategies and investment performance evaluation to assess the practical application value of the models. Since the prediction target in this project is ADA coin returns, which have directional characteristics, we assume investment in a related ADA coin index. Based on the model’s predictions of the index’s upward or downward movement (represented by 1 and 0), there are four trading scenarios: 0-0 represents no position, 0-1 represents entering a position, 1-0 represents closing a position, and 1-1 represents holding a position. The daily returns of each trading day are calculated to evaluate the investment performance of the four prediction systems.
Appendix A.2. Evaluation Metrics
There are two categories of evaluation metrics: one for assessing prediction results and the other for the economic evaluation of investment performance. For prediction results, this study uses Mean Absolute Error (MAE), Mean Squared Error (MSE), Root Mean Squared Error (RMSE), Symmetric Mean Absolute Percentage Error (SMAPE), and the Directional Accuracy Statistic (DSTAT). The relevant formulas are shown in Equation (A1). Here, T represents the number of samples in the test set,
y
t
is the true value at time t,
y
^
t
is the predicted value at time t, and
I
(
)
is an indicator function that takes the value of 1 when the condition is met; otherwise, it takes the value of 0. The economic evaluation metrics for investment performance include the average daily return, maximum drawdown, Sharpe ratio, Sortino ratio, and Calmar ratio. The formulas for calculating the maximum drawdown, Sharpe ratio, Sortino ratio, and Calmar ratio are shown in Equation (A2). In these formulas,
E
r
p
represents the expected return of the asset,
r
f
is the risk-free rate,
σ
p
is the asset volatility,
R
p
,
t
is the sample return below the risk-free rate, and
D
i
and
D
j
are the asset net values at different times.
M
S
E
=
1
/
T
∑
t
=
1
T
y
t
−
y
t
^
2
M
A
E
=
1
/
T
∑
t
=
1
T
y
t
−
y
t
^
R
M
S
E
=
1
/
T
∑
t
=
1
T
y
t
−
y
t
^
2
S
M
A
P
E
=
1
/
T
∑
t
=
1
T
y
t
−
y
t
^
/
y
t
+
y
t
^
2
D
S
T
A
T
=
1
/
T
∑
t
=
1
T
a
t
×
100
%
,
a
t
=
I
y
t
y
t
^
>
0
(A1)
s
h
a
r
p
e
=
E
r
p
−
r
f
/
σ
p
s
o
r
t
i
n
o
=
E
r
p
−
r
f
1
/
(
T
−
1
)
∑
t
=
1
T
R
p
,
t
−
r
f
2
c
a
l
m
a
r
=
(
E
r
p
−
r
f
)
/
max_draw_down
max_draw_down
=
max
D
i
−
D
j
/
D
i
(A2)
The reason for selecting the above metrics to evaluate investment performance is as follows: the average daily return reflects the short-term profitability of the investment portfolio, making it easy to compare different strategies; the maximum drawdown reflects the maximum loss from peak to trough during a specific period, serving as an important risk measure for the strategy; the Sharpe ratio measures the excess returns per unit of total risk (including volatility), which is a classic metric for evaluating risk-adjusted returns; the Sortino ratio considers only downside risk, making it more suitable for assessing the investor’s sensitivity to losses; the Calmar ratio measures the excess returns per unit of maximum drawdown and is useful for evaluating long-term investment strategies’ risk-adjusted returns.
Appendix A.3. Model Confidence Set Test
This research utilizes the Model Confidence Set (MCS) test to evaluate and compare the predictive performance of multiple models within two forecasting systems.
Assume the candidate model set constitutes
M
0
. The purpose of the MCS test is to identify the Model Confidence Set
M
1
−
α
∗
.
M
1
−
α
∗
includes all the best models at the confidence level
1
−
α
. The null hypothesis of the MCS test is
H
0
,
M
:
E
d
i
j
,
t
=
0
,
i
,
j
∈
M
(A3)
In formula (Equation (A3)),
d
i
j
,
t
=
L
i
,
t
−
L
j
,
t
represents the difference sequence of the loss function values between model i and model j. If the null hypothesis
H
0
,
M
is rejected at the confidence level
α
, the MCS test will sequentially eliminate the model with the worst prediction accuracy from the model set
M
. This elimination process will continue until the null hypothesis
H
0
,
M
is no longer rejected at the confidence level
α
. At this point, the remaining models constitute the Model Confidence Set
M
1
−
α
∗
. If the confidence level
α
remains unchanged during each step of the elimination process, then
M
1
−
α
∗
includes the best prediction models based on the
1
−
α
confidence level.
Figure A1.
Hyperparameter graph of GBR in univariate system.
Figure A1.
Hyperparameter graph of GBR in univariate system.
Figure A2.
Hyperparameter graph of RF in univariate system.
Figure A2.
Hyperparameter graph of RF in univariate system.
Figure A3.
Hyperparameter graph of SVR in univariate system.
Figure A3.
Hyperparameter graph of SVR in univariate system.
Figure A4.
Hyperparameter graph of XGB in univariate system.
Figure A4.
Hyperparameter graph of XGB in univariate system.
Figure A5.
Hyperparameter graph of GBR in multivariate system.
Figure A5.
Hyperparameter graph of GBR in multivariate system.
Figure A6.
Hyperparameter graph of RF in multivariate system.
Figure A6.
Hyperparameter graph of RF in multivariate system.
Figure A7.
Hyperparameter graph of SVR in multivariate system.
Figure A7.
Hyperparameter graph of SVR in multivariate system.
Figure A8.
Hyperparameter graph of XGB in multivariate system.
Figure A8.
Hyperparameter graph of XGB in multivariate system.
Figure A9.
Hyperparameter diagram of the high-frequency component of GBR in the “Sliding EMD” system.
Figure A9.
Hyperparameter diagram of the high-frequency component of GBR in the “Sliding EMD” system.
Figure A10.
Hyperparameter diagram of the high-frequency component of RF in the “Sliding EMD” system.
Figure A10.
Hyperparameter diagram of the high-frequency component of RF in the “Sliding EMD” system.
Figure A11.
Hyperparameter diagram of the high-frequency component of SVR in the “Sliding EMD” system.
Figure A11.
Hyperparameter diagram of the high-frequency component of SVR in the “Sliding EMD” system.
Figure A12.
Hyperparameter diagram of the high-frequency component of XGB in the “Sliding EMD” system.
Figure A12.
Hyperparameter diagram of the high-frequency component of XGB in the “Sliding EMD” system.
Figure A13.
Hyperparameter diagram of the low-frequency component of GBR in the “Sliding EMD” system.
Figure A13.
Hyperparameter diagram of the low-frequency component of GBR in the “Sliding EMD” system.
Figure A14.
Hyperparameter diagram of the low-frequency component of RF in the “Sliding EMD” system.
Figure A14.
Hyperparameter diagram of the low-frequency component of RF in the “Sliding EMD” system.
Figure A15.
Hyperparameter diagram of the low-frequency component of SVR in the “Sliding EMD” system.
Figure A15.
Hyperparameter diagram of the low-frequency component of SVR in the “Sliding EMD” system.
Figure A16.
Hyperparameter diagram of the low-frequency component of XGB in the “Sliding EMD” system.
Figure A16.
Hyperparameter diagram of the low-frequency component of XGB in the “Sliding EMD” system.
Figure A17.
The hyperparameter graph of the GBR high-frequency components of the “Sliding EMD–Multi Variables” system.
Figure A17.
The hyperparameter graph of the GBR high-frequency components of the “Sliding EMD–Multi Variables” system.
Figure A18.
The hyperparameter graph of the RF high-frequency components of the “Sliding EMD–Multi Variables” system.
Figure A18.
The hyperparameter graph of the RF high-frequency components of the “Sliding EMD–Multi Variables” system.
Figure A19.
The hyperparameter graph of the SVR high-frequency components of the “Sliding EMD–Multi Variables” system.
Figure A19.
The hyperparameter graph of the SVR high-frequency components of the “Sliding EMD–Multi Variables” system.
Figure A20.
The hyperparameter graph of the XGB high-frequency components of the “Sliding EMD–Multi Variables” system.
Figure A20.
The hyperparameter graph of the XGB high-frequency components of the “Sliding EMD–Multi Variables” system.
Figure A21.
The hyperparameter graph of the GBR low-frequency components of the “Sliding EMD–Multi Variables” system.
Figure A21.
The hyperparameter graph of the GBR low-frequency components of the “Sliding EMD–Multi Variables” system.
Figure A22.
The hyperparameter graph of the RF low-frequency components of the “Sliding EMD–Multi Variables” system.
Figure A22.
The hyperparameter graph of the RF low-frequency components of the “Sliding EMD–Multi Variables” system.
Figure A23.
The hyperparameter graph of the SVR low-frequency components of the “Sliding EMD–Multi Variables” system.
Figure A23.
The hyperparameter graph of the SVR low-frequency components of the “Sliding EMD–Multi Variables” system.
Figure A24.
The hyperparameter graph of the XGB low-frequency components of the “Sliding EMD–Multi Variables” system.
Figure A24.
The hyperparameter graph of the XGB low-frequency components of the “Sliding EMD–Multi Variables” system.
Figure A25.
Multivariate system prediction result graph.
Figure A25.
Multivariate system prediction result graph.
Figure A26.
The Lasso selection relationship coefficient graph of the multivariable system Nasdaq.
Figure A26.
The Lasso selection relationship coefficient graph of the multivariable system Nasdaq.
Figure A27.
The Lasso selection relationship coefficient graph of the multivariable system Sp500.
Figure A27.
The Lasso selection relationship coefficient graph of the multivariable system Sp500.
Figure A28.
The Lasso choice relationship coefficient diagram of Us monetary policy in a multivariate system.
Figure A28.
The Lasso choice relationship coefficient diagram of Us monetary policy in a multivariate system.
Figure A29.
Comparison of prediction accuracy between the “Sliding EMD-Multi Variables” system and the Multivariate Prediction System.
Figure A29.
Comparison of prediction accuracy between the “Sliding EMD-Multi Variables” system and the Multivariate Prediction System.
Figure A30.
Comparison of prediction accuracy between the “Sliding EMD-Multi Variables” system and the Univariate Prediction System.
Figure A30.
Comparison of prediction accuracy between the “Sliding EMD-Multi Variables” system and the Univariate Prediction System.
Table A1.
Error index table of univariate system results.
Table A1.
Error index table of univariate system results.
LR
GBR
RF
SVR
XGB
MSE_1
3.54 × 10
−4
3.62 × 10
−4
3.63 × 10
−4
3.65 × 10
−4
3.60 × 10
−4
RMSE_1
0.0188
0.0190
0.0190
0.0191
0.0190
MAE_1
0.0134
0.0135
0.0135
0.0136
0.0134
SMAPE_1
1.72
1.78
1.74
1.64
1.75
DSTAT_1
0.510
0.489
0.504
0.503
0.493
Table A2.
MCS test result table of multivariate system.
Table A2.
MCS test result table of multivariate system.
Index
Comparison_2&1
T
R
T
S
Q
1
SVR_2 (0.000)
SVR_2 (0.000)
2
LR_2 (0.000)
LR_2 (0.003)
3
RF_2 (0.018)
RF_2 (0.159 *)
4
SVR_1 (0.061)
SVR_1 (0.269 **)
5
RF_1 (0.186 *)
RF_1 (0.377 **)
6
GBR_1 (0.288 **)
GBR_1 (0.448 **)
7
XGB_1 (0.377 **)
XGB_1 (0.530 **)
8
XGB_2 (0.564 **)
XGB_2 (0.676 **)
9
LR_1 (0.866 **)
LR_1 (0.866 **)
10
GBR_2 (1.000 **)
GBR_2 (1.000 **)
Note:
** and * denote statistical significance at the 5% and 10% levels, respectively.
Table A3.
The result table of Maximum Drawdown Ratio of the “Sliding EMD” system.
Table A3.
The result table of Maximum Drawdown Ratio of the “Sliding EMD” system.
Maximum Drawdown Ratio
Comparison_3&1
Comparison_3&2
LR
0.165
0.629
GBR
0.199
0.366
RF
0.247
0.519
SVR
0.165
0.527
XGB
0.198
0.300
Table A4.
The result table of Sharpe Ratio of the “Sliding EMD” system.
Table A4.
The result table of Sharpe Ratio of the “Sliding EMD” system.
Sharpe Ratio
Comparison_3&1
Comparison_3&2
LR
0.0371
3.77
GBR
0.297
0.314
RF
0.687
1.42
SVR
0.239
2.54
XGB
0.533
0.413
Table A5.
The Sortino Ratio result table of the “Sliding EMD” system.
Table A5.
The Sortino Ratio result table of the “Sliding EMD” system.
Sortino Ratio
Comparison_3&1
Comparison_3&2
LR
0.0905
8.69
GBR
0.764
0.857
RF
1.79
3.91
SVR
0.665
6.71
XGB
1.44
1.17
Table A6.
The Calmar Ratio result table of the “Sliding EMD” system.
Table A6.
The Calmar Ratio result table of the “Sliding EMD” system.
Calmar Ratio
Comparison_3&1
Comparison_3&2
LR
0.0579
0.551
GBR
0.128
0.0573
RF
0.228
0.330
SVR
0.109
0.475
XGB
0.230
0.138
Table A7.
The result table of the Maximum Drawdown Ratio of the “Sliding EMD-Multi Variables” system.
Table A7.
The result table of the Maximum Drawdown Ratio of the “Sliding EMD-Multi Variables” system.
Maximum Drawdown Ratio
Comparison_4&1
Comparison_4&2
Comparison_4&3
LR
−0.0173
0.447
−0.182
GBR
0.0961
0.264
−0.102
RF
0.277
0.549
0.0299
SVR
0.293
0.655
0.128
XGB
0.180
0.281
−0.0181
Table A8.
The result table of Sharpe Ratio of the “Sliding EMD-Multi Variables” system.
Table A8.
The result table of Sharpe Ratio of the “Sliding EMD-Multi Variables” system.
Sharpe Ratio
Comparison_4&1
Comparison_4&2
Comparison_4&3
LR
−0.385
3.34
−0.422
GBR
−0.0500
0.0671
−0.247
RF
0.760
1.50
0.0732
SVR
0.470
2.78
0.231
XGB
−0.224
0.0562
−0.357
Table A9.
The Sortino Ratio result table of the “Sliding EMD-Multi Variables” system.
Table A9.
The Sortino Ratio result table of the “Sliding EMD-Multi Variables” system.
Sortino Ratio
Comparison_4&1
Comparison_4&2
Comparison_4&3
LR
−1.12
7.48
−1.21
GBR
0.0465
0.139
−0.718
RF
2.04
4.15
0.250
SVR
1.39
7.44
0.726
XGB
0.445
0.171
−0.992
Table A10.
The Calmar Ratio result table of the “Sliding EMD-Multi Variables” system.
Table A10.
The Calmar Ratio result table of the “Sliding EMD-Multi Variables” system.
Calmar Ratio
Comparison_4&1
Comparison_4&2
Comparison_4&3
LR
−0.144
0.349
−0.202
GBR
0.0412
−0.0296
−0.0868
RF
0.252
0.354
0.0242
SVR
0.202
0.568
0.0924
XGB
0.0498
−0.0423
−0.180
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Figure 5.
Figure of the ADA daily closing price and return series.
Figure 5.
Figure of the ADA daily closing price and return series.
Figure 6.
The time series graph of the four main variables. Note:
Figure 5
and
Figure 6
are plotted by the authors based on raw data collected from multiple sources.
Figure 6.
The time series graph of the four main variables. Note:
Figure 5
and
Figure 6
are plotted by the authors based on raw data collected from multiple sources.
Figure 7.
LASSO dynamic factor selection results for high-frequency components. Note:
Figure 7
,
Figure 8
,
Figure 9
and
Figure 10
illustrate the LASSO-based dynamic factor selection results and their time-varying coefficients, and were produced by the authors.
Figure 7.
LASSO dynamic factor selection results for high-frequency components. Note:
Figure 7
,
Figure 8
,
Figure 9
and
Figure 10
illustrate the LASSO-based dynamic factor selection results and their time-varying coefficients, and were produced by the authors.
Figure 8.
Dynamic coefficient plot of high-frequency factors in the “Sliding EMD–Multi Variables” prediction system.
Figure 8.
Dynamic coefficient plot of high-frequency factors in the “Sliding EMD–Multi Variables” prediction system.
Figure 9.
LASSO dynamic factor plot for low-frequency components.
Figure 9.
LASSO dynamic factor plot for low-frequency components.
Figure 10.
Dynamic coefficient plot of low-frequency factors in the “Sliding EMD–Multi Variables” prediction system.
Figure 10.
Dynamic coefficient plot of low-frequency factors in the “Sliding EMD–Multi Variables” prediction system.
Figure 11.
Comparison of prediction accuracy between the “Sliding EMD” system and the Univariate Prediction System. Note: The radar chart shows percentage data. The closer to the center of the origin, the smaller the data becomes. The further out the data, the greater the percentage, and the stronger the improvement percentage in the comparison between the two systems.
Figure 11.
Comparison of prediction accuracy between the “Sliding EMD” system and the Univariate Prediction System. Note: The radar chart shows percentage data. The closer to the center of the origin, the smaller the data becomes. The further out the data, the greater the percentage, and the stronger the improvement percentage in the comparison between the two systems.
Table 1.
Error metrics for the Multivariate Prediction System.
Table 1.
Error metrics for the Multivariate Prediction System.
LR
GBR
RF
SVR
XGB
MSE_2
4.05 × 10
−4
3.52 × 10
−4
3.71 × 10
−4
4.13 × 10
−4
3.59 × 10
−4
RMSE_2
0.0201
0.0188
0.0193
0.0203
0.0189
MAE_2
0.0145
0.0133
0.0136
0.0146
0.0134
SMAPE_2
1.73
1.74
1.73
1.73
1.74
DSTAT_2
0.381
0.487
0.447
0.367
0.482
Table 2.
Comparison of the Multivariate Prediction System with the Univariate Prediction System.
Table 2.
Comparison of the Multivariate Prediction System with the Univariate Prediction System.
Comparison_2&1
LR
GBR
RF
SVR
XGB
MSE_21
−14.46%
2.64%
−2.17%
−13.41%
0.29%
RMSE_21
−6.98%
1.33%
−1.08%
−6.49%
0.15%
MAE_21
−8.25%
1.57%
−0.83%
−7.53%
0.18%
SMAPE_21
−1.03%
2.07%
0.60%
−5.23%
0.73%
DSTAT_21
−25.26%
−0.26%
−11.35%
−26.97%
−2.29%
Note: A “−” indicates worse forecast performance.
Table 3.
Error metrics for the “Sliding EMD” system.
Table 3.
Error metrics for the “Sliding EMD” system.
LR
GBR
RF
SVR
XGB
MSE_3
3.53 × 10
−4
3.57 × 10
−4
3.58 × 10
−4
3.62 × 10
−4
3.57 × 10
−4
RMSE_3
0.0188
0.0189
0.0189
0.0190
0.0189
MAE_3
0.0134
0.0135
0.0135
0.0136
0.0135
SMAPE_3
1.64
1.66
1.64
1.59
1.65
DSTAT_3
0.510
0.500
0.494
0.504
0.500
Table 4.
MCS test results for the “Sliding EMD” system.
Table 4.
MCS test results for the “Sliding EMD” system.
Index
Comparison_3&1
Comparison_3&2
T
R
T
S
Q
T
R
T
S
Q
1
SVR_1 (0.168 *)
SVR_1 (0.182 *)
SVR_2 (0.000)
SVR_2 (0.000)
2
RF_1 (0.255 **)
RF_1 (0.270 **)
LR_2 (0.000)
LR_2 (0.000)
3
SVR_3 (0.255 **)
SVR_3 (0.305 **)
RF_2 (0.016)
RF_2 (0.208 **)
4
GBR_1 (0.438 **)
GBR_1 (0.424 **)
SVR_3 (0.134 *)
SVR_3 (0.396 **)
5
XGB_1 (0.629 **)
XGB_1 (0.538 **)
RF_3 (0.633 **)
RF_3 (0.657 **)
6
RF_3 (0.659 **)
RF_3 (0.546 **)
GBR_3 (0.633 **)
GBR_3 (0.657 **)
7
GBR_3 (0.659 **)
GBR_3 (0.550 **)
XGB_2 (0.633 **)
XGB_2 (0.657 **)
8
XGB_3 (0.659 **)
XGB_3 (0.550 **)
XGB_3 (0.633 **)
XGB_3 (0.657 **)
9
LR_1 (0.868 **)
LR_1 (0.868 **)
LR_3 (0.934 **)
LR_3 (0.934 **)
10
LR_3 (1.000 **)
LR_3 (1.000 **)
GBR_2 (1.000 **)
GBR_2 (1.000 **)
Note:
In
Table 4
and in subsequent tables presenting Model Confidence Set test results, asterisks indicate the following significance levels: * denotes significance at α = 0.05, and ** denotes significance at α = 0.01.
Table 5.
Daily return comparison for the “Sliding EMD” system.
Table 5.
Daily return comparison for the “Sliding EMD” system.
Daily Return
Comparison_3&1
Comparison_3&2
LR
9.00 × 10
−5
2.64 × 10
−3
GBR
3.63 × 10
−4
3.76 × 10
−4
RF
5.74 × 10
−4
1.35 × 10
−3
SVR
2.50 × 10
−4
2.27 × 10
−3
XGB
5.43 × 10
−4
4.24 × 10
−4
Table 6.
Error metrics for the “Sliding EMD–Multi Variables” system.
Table 6.
Error metrics for the “Sliding EMD–Multi Variables” system.
LR
GBR
RF
SVR
XGB
MSE_4
3.50 × 10
−4
3.57 × 10
−4
3.56 × 10
−4
3.56 × 10
−4
3.56 × 10
−4
RMSE_4
0.0187
0.0189
0.0189
0.0189
0.0189
MAE_4
0.0133
0.0135
0.0135
0.0135
0.0135
SMAPE_4
1.68
1.68
1.68
1.67
1.69
DSTAT_4
0.507
0.485
0.504
0.514
0.493
Table 7.
MCS test results for the “Sliding EMD–Multi Variables” system.
Table 7.
MCS test results for the “Sliding EMD–Multi Variables” system.
Index
Comparison_4&1
Comparison_4&2
Comparison_4&3
T
R
T
S
Q
T
R
T
S
Q
T
R
T
S
Q
1
SVR_1 (0.105 *)
SVR_1 (0.108 *)
SVR_2 (0.000)
SVR_2 (0.000)
SVR_3 (0.275 **)
SVR_3 (0.222 **)
2
RF_1 (0.312 **)
RF_1 (0.187 *)
LR_2 (0.000)
LR_2 (0.000)
GBR_4 (0.309 **)
GBR_4 (0.327 **)
3
GBR_1 (0.312 **)
GBR_1 (0.253 **)
RF_2 (0.016)
RF_2 (0.224 **)
RF_3 (0.309 **)
RF_3 (0.327 **)
4
GBR_4 (0.312 **)
GBR_4 (0.283 **)
GBR_4 (0.188 *)
GBR_4 (0.456 **)
XGB_4 (0.309 **)
XGB_4 (0.327 **)
5
XGB_1 (0.312 **)
XGB_1 (0.283 **)
XGB_4 (0.188 *)
XGB_4 (0.462 **)
RF_4 (0.494 **)
RF_4 (0.327 **)
6
XGB_4 (0.312 **)
XGB_4 (0.283 **)
SVR_4 (0.351 **)
SVR_4 (0.518 **)
GBR_3 (0.494 **)
GBR_3 (0.327 **)
7
SVR_4 (0.312 **)
SVR_4 (0.283 **)
XGB_2 (0.351 **)
XGB_2 (0.518 **)
SVR_4 (0.494 **)
SVR_4 (0.327 **)
8
RF_4 (0.312 **)
RF_4 (0.283 **)
RF_4 (0.351 **)
RF_4 (0.518 **)
XGB_3 (0.494 **)
XGB_3 (0.327 **)
9
LR_1 (0.488 **)
LR_1 (0.488 **)
GBR_2 (0.997 **)
GBR_2 (0.997 **)
LR_3 (0.520 **)
LR_3 (0.520 **)
10
LR_4 (1.000 **)
LR_4 (1.000 **)
LR_4 (1.000 **)
LR_4 (1.000 **)
LR_4 (1.000 **)
LR_4 (1.000 **)
Note:
In
Table 7
, asterisks indicate the following significance levels: * denotes significance at α = 0.05, and ** denotes significance at α = 0.01.
Table 8.
Comparison with the most relevant studies.
Table 8.
Comparison with the most relevant studies.
Study (Year)
Method
Sliding Window?
Other Predictive Variables?
Potential Future
Data Leakage?
Key Empirical Findings/Investment Implications
1
Xu and Niu (2023) [
13
]
EMD/VMD-KNN
Yes
Yes (not enough)
No, sliding ensures real-time updates
Decomposition–reconstruction method helps filter out noise from crude oil price time series, improving the prediction accuracy.
2
Kim et al. (2021) [
25
]
SVR, RF, XGB
No
Yes (only one type
of variable)
Yes, full-sample data used
Combining Blockchain data with machine learning algorithms significantly improves the accuracy of Ethereum price forecasts. Investors can analyze Blockchain data, leading to better entry/exit points in the market.
3
Fallah et al. (2024) [
26
]
LSTM-GRU
Yes
Yes (not enough)
No, sliding ensures real-time updates
Integrating error correction mechanisms into deep learning models improves the prediction accuracy for cryptocurrency prices. This model can provide more accurate price predictions, reducing risk and enhancing decision-making.
4
Wang et al. (2023) [
23
]
SVM, GBR
Yes
Yes (only three types of variables)
No, sliding ensures real-time updates
Machine learning models, when combined with both internal and external determinants, can significantly improve the prediction of cryptocurrency volatility. Investors can use these insights to better improve risk management and trading strategies.
5
Qiu et al. (2025) [
24
]
ARIMA-GARCH-LSTM
Yes
Yes (only three types of variables)
No, sliding ensures real-time updates
The model clustering approach enhances volatility forecasting by combining the strengths of multiple models. Investors can use this approach to gain a more reliable forecast of cryptocurrency volatility.
6
Zhang et al. (2023) [
12
]
VMD-GRU
Yes
Yes (not enough)
No, sliding ensures real-time updates
The model provides improved accuracy in forecasting oil prices by effectively capturing both short-term and long-term trends in the price movements. This approach offers oil traders and investors a powerful tool for predicting price movements, improving trading strategies and hedging decisions.
7
Li et al. (2022) [
28
]
LR
No
Yes (enough)
Yes, full-sample data used
The study finds that art pricing can be effectively modeled by considering both historical returns and risk factors. Investors in the art market can use these insights to assess the risk and return potential of artworks at auction.
8
Hajek et al. (2023) [
42
]
RF-XGB-Gradient Boosting
Yes
Yes (enough)
No, sliding ensures real-time updates
The study demonstrates that investor sentiment can significantly improve the prediction of Bitcoin prices. Investors can predict price trends more accurately by considering both market data and sentiment, leading to better timing for Bitcoin investments.
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Open AccessArticle
# Cryptocurrency Price Prediction Using Sliding Empirical Mode Decomposition with Economic Variables: A Machine Learning Approach
by
Wenhao Zhang
Wenhao Zhang
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1,
Zhenpeng Tang
Zhenpeng Tang
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1,†,
Xiaowen Zhuang
Xiaowen Zhuang
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Baihua Dong
Baihua Dong
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1
College of Economics and Management, Fujian Agriculture and Forestry University, Fuzhou 350002, China
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College of Landscape Architecture and Art, Fujian Agriculture and Forestry University, Fuzhou 350002, China
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The Bartlett School of Sustainable Construction, University College London, London WC1E 7HB, UK
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*Fractal Fract.* **2026**, *10*(4), 218; <https://doi.org/10.3390/fractalfract10040218>
Submission received: 6 January 2026 / Revised: 30 January 2026 / Accepted: 11 February 2026 / Published: 26 March 2026
(This article belongs to the Section [Optimization, Big Data, and AI/ML](https://www.mdpi.com/journal/fractalfract/sections/Optimization_Big_Data_AIML))
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## Abstract
The cryptocurrency market has attracted significant attention from global investors, with Cardano (ADA) ranking among the top cryptocurrencies by market capitalization. However, predicting ADA returns remains challenging due to the complex, multi-scale dynamics influenced by Federal Reserve policies, geopolitical events, and high-frequency trading. This study proposes a “Sliding EMD–Multi Variables” framework for cryptocurrency return prediction, leveraging Empirical Mode Decomposition’s multi-scale fractal properties to capture nonlinear dynamics at different time scales. The sliding window decomposition method addresses data leakage issues while incorporating key economic and policy variables at the component level. The empirical results demonstrate that the Sliding EMD system significantly outperforms univariate and multivariate benchmarks. Compared to the univariate system, it improves MSE, RMSE, SMAPE, and DSTAT by 0.83%, 0.42%, 5.23%, and 0.43%, respectively, while enhancing investment metrics (maximum drawdown, Sharpe ratio, Sortino ratio, Calmar ratio) by 0.19, 0.36, 0.95, and 0.15. Against the multivariate system, improvements reach 5.52%, 3.14%, 5.74%, and 17.62% in prediction accuracy, with investment performance gains of 0.47, 1.69, 4.27, and 0.31. Incorporating economic variables at the component level yields additional improvements of 0.94%, 0.47%, and 0.78% in MSE, RMSE, and MAE. These findings offer valuable insights for cryptocurrency portfolio optimization using fractal-based decomposition methods.
Keywords:
[sliding empirical mode decomposition](https://www.mdpi.com/search?q=sliding+empirical+mode+decomposition); [fractal time series analysis](https://www.mdpi.com/search?q=fractal+time+series+analysis); [cryptocurrency return forecasting](https://www.mdpi.com/search?q=cryptocurrency+return+forecasting); [multi-scale decomposition](https://www.mdpi.com/search?q=multi-scale+decomposition)
## 1\. Introduction
Cardano cryptocurrency (ADA) holds a significant position in the cryptocurrency market, ranking among the top ten globally with a market capitalization of around 26.17 billion USD. Its growing institutional recognition is underscored by major financial infrastructure developments, such as CME Group’s announced plan to launch ADA-linked futures contracts, reflecting its established liquidity and maturation within the digital asset ecosystem (<https://www.nasdaq.com/press-release/cme-group-expand-crypto-derivatives-suite-launch-cardano-chainlink-and-stellar>, accessed on 15 January 2026). Cardano utilizes the Ouroboros proof-of-stake consensus mechanism, which its founder estimates consumes less than 0.01% of the energy compared to the Bitcoin network (<https://www.the-independent.com/space/cardano-crypto-bitcoin-elon-musk-b1849021.html>, accessed on 18 May 2021). This energy efficiency has drawn the attention of investors focused on ESG (Environmental, Social, and Governance) criteria \[[1](https://www.mdpi.com/2504-3110/10/4/218#B1-fractalfract-10-00218)\].
ADA’s price volatility is highly susceptible to shifts in macroeconomic conditions and broader financial environments. Elsayed et al. (2022) \[[2](https://www.mdpi.com/2504-3110/10/4/218#B2-fractalfract-10-00218)\] found a synergistic effect between the macroeconomic environment and cryptocurrency trading volumes. Feng et al. (2025) \[[3](https://www.mdpi.com/2504-3110/10/4/218#B3-fractalfract-10-00218)\] argued that changes in regulatory policies have increased the volatility of cryptocurrency prices. Aharon et al. (2021) \[[4](https://www.mdpi.com/2504-3110/10/4/218#B4-fractalfract-10-00218)\] discovered a dynamic correlation between the US dollar exchange rate and cryptocurrency prices. There is also risk contagion between different cryptocurrencies \[[5](https://www.mdpi.com/2504-3110/10/4/218#B5-fractalfract-10-00218)\]. Moreover, the connections between traditional financial markets and cryptocurrencies have become more frequent \[[6](https://www.mdpi.com/2504-3110/10/4/218#B6-fractalfract-10-00218)\]. Consequently, incorporating such external determinants into forecasting models is crucial for improving prediction performance and understanding the multi-scale drivers of ADA prices.
The volatility of ADA prices and its impact on the economy and financial markets have attracted significant academic attention. ADA’s market value fluctuations affect the consumption sector through wealth effects and, via chain reactions, influence upstream and downstream companies in the blockchain industry \[[7](https://www.mdpi.com/2504-3110/10/4/218#B7-fractalfract-10-00218)\]. This price instability increases the systemic risk premium in the cryptocurrency market, transferring risk to the traditional financial system through cross-market correlations. Notably, ADA’s price exhibits volatility clustering, long-range dependence, and multifractal characteristics across different time scales, reflecting the complex nonlinear dynamics inherent in cryptocurrency markets \[[8](https://www.mdpi.com/2504-3110/10/4/218#B8-fractalfract-10-00218)\]. These multi-scale fractal properties challenge classical financial time series models that assume linear relationships and stationary processes. As a result, developing a stable and reliable prediction system that accounts for multi-scale dynamics is crucial for ADA.
Current cryptocurrency price prediction methods have evolved from traditional econometric models to machine learning techniques and “decomposition–ensemble” hybrid methods \[[9](https://www.mdpi.com/2504-3110/10/4/218#B9-fractalfract-10-00218)\]. Econometric models face limitations in capturing non-linear features \[[10](https://www.mdpi.com/2504-3110/10/4/218#B10-fractalfract-10-00218)\], while machine learning methods can excel in modeling complex patterns \[[11](https://www.mdpi.com/2504-3110/10/4/218#B11-fractalfract-10-00218)\]. However, when dealing with multi-scale, nonlinear signal data like cryptocurrency returns, even single machine learning algorithms may not achieve ideal predictive performance without using hybrid models like “decomposition–ensemble” \[[12](https://www.mdpi.com/2504-3110/10/4/218#B12-fractalfract-10-00218)\].
The “decomposition and ensemble” framework, rooted in multi-scale signal processing and fractal analysis, can decompose complex financial signals into multiple frequency components corresponding to different time scales. This multi-resolution approach aligns with the hierarchical structure of financial market dynamics, where short-term trading behavior and long-term macroeconomic trends operate at distinct temporal scales. Next, it applies ensemble-based recombination techniques to filter out extraneous noise. By forecasting each meaningful component separately and then summing those forecasts, this “divide-and-conquer” approach improves the accuracy of detecting complex multi-scale dynamics. However, decomposition methods applied to the full sample may result in information leakage, as the decomposition of historical data points can be influenced by the statistical properties of future data when the entire series is processed at once, thereby contaminating the training set with information that would not be available in a realistic sliding forecasting setting. Several scholars have explored algorithms like sliding VMD and sliding EEMD for financial asset price prediction \[[13](https://www.mdpi.com/2504-3110/10/4/218#B13-fractalfract-10-00218)\]. However, research on applying sliding decomposition algorithms that preserve the temporal hierarchy to cryptocurrency return prediction is still limited. To address the information leakage issue inherent in full-sample decomposition, the sliding window approach processes data sequentially, ensuring that each training set uses only information available up to that point. This preserves the temporal hierarchy and prevents future information from contaminating the prediction process, making it a methodologically sound framework for cryptocurrency return forecasting. Additionally, incorporating essential factors, such as key policy and economic variables, at different frequency scales into sliding decomposition algorithms will enhance the understanding of the multi-scale drivers of ADA prices and assist cryptocurrency market investors in optimizing their portfolios.
To address the limitations mentioned above, this study focuses on the following questions: Does sliding decomposition that captures multi-scale dynamics improve the accuracy of ADA return predictions compared to traditional non-decomposed frameworks? Based on the existing literature, can incorporating key economic variables at the component level across different time scales into the prediction model enhance the forecasting performance for ADA? Which method, variable-driven or multi-scale sliding decomposition, leads to greater improvements in prediction? Can investment performance based on fractal-based sliding decomposition provide better results, helping investors make more informed decisions?
This research evaluates and compares four different forecasting frameworks: a Univariate Prediction System (System 1), a Multivariate Prediction System (System 2), the “Sliding EMD” prediction system (System 3), and the “Sliding EMD–Multi Variables” prediction system (System 4). Comparing System 2 with System 1 allows for testing whether incorporating influencing factors into the raw ADA series improves prediction accuracy. The comparison between System 3 and System 1 examines whether the Sliding EMD that captures multi-scale fractal properties can improve forecasting accuracy compared to a non-decomposed univariate system. The comparison between System 3 and System 2 demonstrates the relative advantages of multivariate and multi-scale decomposition approaches. Lastly, the comparison between System 4 and System 3 tests whether incorporating factors at the component level across different frequency scales in the “Sliding EMD” framework can further enhance prediction.
The innovation of this study lies in the following aspects: First, this study directly compares the “Sliding EMD” framework that exploits multi-scale temporal structures with traditional frameworks to evaluate the effectiveness of sliding decomposition technology in ADA prediction. To avoid the data leakage issue caused by applying traditional full-sample decomposition algorithms to ADA returns, this study uses the Sliding EMD method with a fixed window to predict ADA returns. Unlike existing studies that apply sliding decomposition, we employ unsupervised K-means clustering to adaptively group the derived components into high- and low-frequency clusters based on their intrinsic statistical properties. This clustering approach leverages the natural frequency separation inherent in EMD’s multi-scale decomposition, allowing us to capture both rapid market fluctuations and gradual trend movements. This approach not only integrates information from different frequency components to enhance prediction performance but also lays the foundation for further incorporating the impact of economic variables on different frequency scales.
Second, leveraging existing research on ADA’s influential factors, seven main categories of influencing variables are identified: macroeconomic variables, social variables, exchange rate variables, competitive variables, financial variables, commodity variables, and policy variables. Using Least Absolute Shrinkage and Selection Operator (LASSO) regression, significant variables influencing both the raw returns and decomposed components at different time scales are determined. The dynamic factor selection process using LASSO can be integrated into the Univariate Prediction System to form a Multivariate Prediction System. When incorporated into the “Sliding EMD” system, this results in the “Sliding EMD–Multi Variables” system that accounts for scale-dependent economic influences.
Finally, based on rigorous error metrics and statistical tests, this study yields three key insights that advance our understanding of ADA return forecasting. First, the multi-scale Sliding EMD framework exerts a stronger influence on prediction accuracy than dynamic factor selection via LASSO. Second, the prediction performance of the Sliding EMD system consistently surpasses that of the multivariate system. Third, the “Sliding EMD–Multi Variables” system delivers a slight improvement over the “Sliding EMD” system, further enhancing forecasting accuracy. This system integrates fractal-based decomposition with scale-specific economic variables, while the conventional multivariate approach proves comparatively ineffective. These findings collectively affirm that the predictability of ADA returns is fundamentally shaped by economic factors operating across distinct frequency components and time scales. To demonstrate the practical utility of these insights, we conduct an investment performance analysis, which confirms that the proposed framework aids investors in optimizing portfolio allocation, enhancing risk-adjusted returns, and mitigating downside risk, thereby offering actionable guidance for financial decision-making.
The structure of this paper is as follows: [Section 2](https://www.mdpi.com/2504-3110/10/4/218#sec2-fractalfract-10-00218) provides a literature review on the main drivers and prediction methods for ADA; [Section 3](https://www.mdpi.com/2504-3110/10/4/218#sec3-fractalfract-10-00218) details the four prediction frameworks employed in this study for ADA returns; [Section 4](https://www.mdpi.com/2504-3110/10/4/218#sec4-fractalfract-10-00218) analyzes ADA returns and key variables used in this study, with a discussion on the variables selected via LASSO; [Section 5](https://www.mdpi.com/2504-3110/10/4/218#sec5-fractalfract-10-00218) presents a comparison of the prediction results of the four frameworks for ADA returns, performance tests, and corresponding investment performance comparisons; [Section 6](https://www.mdpi.com/2504-3110/10/4/218#sec6-fractalfract-10-00218) discusses the research findings; and [Section 7](https://www.mdpi.com/2504-3110/10/4/218#sec7-fractalfract-10-00218) concludes the study with investment insights.
## 2\. Literature Review
### 2\.1. Key Drivers of ADA Price
As a prominent cryptocurrency, ADA exhibits significant return correlations with other major digital assets. This interdependence stems from shared market mechanisms and investor psychology. Specifically, price appreciation in large-capitalization cryptocurrencies such as Bitcoin and Ethereum, which is typically driven by institutional inflows, favorable regulatory developments, or broader macroeconomic tailwinds, tends to increase overall market risk appetite. This shift in sentiment encourages capital to flow across the cryptocurrency ecosystem, activating price transmission channels that subsequently elevate ADA’s valuation \[[7](https://www.mdpi.com/2504-3110/10/4/218#B7-fractalfract-10-00218)\]. Moreover, ADA is primarily traded against Bitcoin (ADA/BTC) and stablecoins such as USDT (ADA/USDT). Consequently, pronounced fluctuations in Bitcoin often induce passive, correlation-driven adjustments in the ADA/BTC pair, while ADA/USDT valuations remain additionally exposed to shifts in overall market sentiment and liquidity conditions \[[14](https://www.mdpi.com/2504-3110/10/4/218#B14-fractalfract-10-00218)\].
ADA’s price dynamics are significantly shaped by macroeconomic and policy variables, including exchange rates, economic uncertainty indices, and fiscal and monetary policies. Exchange-rate movements, particularly in the U.S. dollar, exert a notable pressure on cryptocurrency valuations: a strengthening dollar typically dampens investor appetite for risk assets, leading to downward pressure on ADA’s price \[[4](https://www.mdpi.com/2504-3110/10/4/218#B4-fractalfract-10-00218)\]. Concurrently, heightened economic policy uncertainty elevates perceived risk within the cryptocurrency sector, which further suppresses ADA’s market performance \[[2](https://www.mdpi.com/2504-3110/10/4/218#B2-fractalfract-10-00218)\]. Conversely, ADA may serve as an effective inflation-hedging instrument; rising inflation expectations often drive capital toward cryptocurrencies as stores of value, thereby boosting ADA’s price \[[15](https://www.mdpi.com/2504-3110/10/4/218#B15-fractalfract-10-00218)\]. Moreover, accommodative fiscal and monetary policies stimulate liquidity and risk-taking sentiment, indirectly fostering bullish conditions in the cryptocurrency market and supporting ADA’s upward momentum \[[16](https://www.mdpi.com/2504-3110/10/4/218#B16-fractalfract-10-00218)\].
The price of ADA is notably influenced by developments in both financial and commodity markets. In equity markets, fluctuations in stock prices can generate spillover effects on cryptocurrency valuations. As demonstrated by Attarzadeh et al. (2024) \[[17](https://www.mdpi.com/2504-3110/10/4/218#B17-fractalfract-10-00218)\], a measurable transmission of volatility and returns from traditional equities to ADA exists, a linkage that typically reflects concurrent shifts in broader risk sentiment and liquidity conditions affecting both asset classes. Meanwhile, commodity markets exert influence through a more structural channel, since the operational costs of blockchain networks depend substantially on hardware components, including specialized metals used in mining hardware and energy consumption, whose prices are tied directly to commodity cycles. Rising costs in these inputs, as noted by Jiang et al. (2025) \[[18](https://www.mdpi.com/2504-3110/10/4/218#B18-fractalfract-10-00218)\], can constrain network expansion and operational efficiency, thereby indirectly pressuring the valuation of cryptocurrencies such as ADA.
Online sentiment and extreme events constitute critical external drivers of ADA’s price dynamics. Investor attention, often proxied by search volumes on platforms such as Google, reflects real-time shifts in retail and speculative interest. As noted by Aslanidis et al. (2024) \[[19](https://www.mdpi.com/2504-3110/10/4/218#B19-fractalfract-10-00218)\] and Hoang et al. (2024) \[[20](https://www.mdpi.com/2504-3110/10/4/218#B20-fractalfract-10-00218)\], this attention can rapidly translate into trading pressure and price momentum for cryptocurrencies including ADA. Beyond mere attention metrics, broader sentiment extracted from social media and news coverage further amplifies short-term volatility, as herd behavior frequently characterizes cryptocurrency markets. Extreme events, including geopolitical conflicts, trade disputes, or large-scale natural disasters, introduce sudden uncertainty and risk-off sentiment across global markets, triggering pronounced fluctuations in cryptocurrency valuations. Moreover, regulatory and policy announcements, particularly from influential jurisdictions like the United States, directly shape market structure and investor confidence. Będowska et al. (2024) \[[21](https://www.mdpi.com/2504-3110/10/4/218#B21-fractalfract-10-00218)\] highlight that the official stance of U.S. authorities toward digital assets can alter liquidity conditions, institutional participation, and long-term adoption prospects, thereby exerting a sustained influence on ADA’s market trajectory.
Time-scale decomposition is theoretically and empirically essential for cryptocurrency forecasting, as it aligns with the Heterogeneous Market Hypothesis (HMH). The HMH posits that market participants operate on distinct investment horizons, driving price formation at multiple frequencies. Low-frequency components predominantly reflect fundamental macroeconomic forces, which evolve slowly and anchor the intrinsic value of assets. In contrast, high-frequency components capture transient market microstructure noise, including speculative trading, liquidity shocks, and immediate reactions to exogenous events. By isolating these frequency bands, predictive models can disentangle the distinct economic mechanisms at play: macroeconomic fundamentals govern long-term trends, while short-term volatility is driven by information asymmetry and behavioral factors \[[22](https://www.mdpi.com/2504-3110/10/4/218#B22-fractalfract-10-00218)\]. This separation not only enhances forecast accuracy by reducing noise interference but also provides critical insights into cryptocurrency market dynamics, such as the differential impact of financial factors (high-frequency) versus monetary and fiscal policies (low-frequency). Thus, frequency-aware modeling is not merely a technical refinement, but also a theoretically grounded necessity for robust cryptocurrency prediction.
The existing literature has identified numerous economic and financial factors affecting ADA returns, yet seldom integrates them dynamically into predictive models. This limits both explanatory power and forecast accuracy. Our study addresses this gap by implementing a factor-informed prediction architecture that combines sliding window decomposition with LASSO-based dynamic variable selection. This approach captures scale-dependent and time-varying effects of key drivers, enhances interpretability, and provides an actionable framework for improving prediction accuracy and supporting investment decisions.
### 2\.2. Cryptocurrency Price Prediction Methods
Forecasting cryptocurrency asset prices can be clearly divided into three approaches: traditional econometric models, machine learning, and the “decomposition–ensemble” system \[[23](https://www.mdpi.com/2504-3110/10/4/218#B23-fractalfract-10-00218)\]. Traditional econometric models mainly include ARIMA, GARCH family, and HAR family models \[[24](https://www.mdpi.com/2504-3110/10/4/218#B24-fractalfract-10-00218)\]. However, these models have strict assumptions, such as the linearity and stationarity of time series. Although some econometric models have developed new methods applicable to nonlinear data, overall, econometric models still exhibit significant limitations when it comes to capturing the complex financial time series signals of cryptocurrencies.
Machine learning emerged in the context of big data and artificial intelligence, with traditional machine learning algorithms such as Support Vector Machines (SVMs), Random Forest (RF), and Gradient Boosting Decision Trees (GBDTs) being commonly used in financial asset price prediction \[[25](https://www.mdpi.com/2504-3110/10/4/218#B25-fractalfract-10-00218)\]. Long Short-Term Memory (LSTM) networks and Convolutional Neural Networks (CNNs) are classic deep learning algorithms for cryptocurrency prediction \[[26](https://www.mdpi.com/2504-3110/10/4/218#B26-fractalfract-10-00218)\]. Overall, both traditional machine learning and deep learning can effectively capture the nonlinear characteristics of time series. However, in the 24/7 cryptocurrency market, the complex, chaotic features still compel researchers to turn to the development of hybrid models.
While deep learning models such as LSTM and GRU can capture complex nonlinear patterns in cryptocurrency forecasting, they frequently exhibit prediction instability manifested through output oscillations and heightened sensitivity to initialization and hyperparameter configurations \[[27](https://www.mdpi.com/2504-3110/10/4/218#B27-fractalfract-10-00218)\]. Though tree-based ensemble methods (Random Forest, Gradient Boosting Regressor, XGBoost, and so on) are comparatively less flexible in modeling highly intricate relationships, they deliver markedly more stable and reproducible predictions.
The “decomposition–ensemble” system effectively handles the complexity of financial time series and has shown promising results in previous studies. Standard decomposition algorithms include Empirical Mode Decomposition (EMD), Variational Mode Decomposition (VMD), and Wavelet Transform (WT) \[[28](https://www.mdpi.com/2504-3110/10/4/218#B28-fractalfract-10-00218)\]. By decomposing complex time series into components of different frequencies, predicting each component separately, and then aggregating the results, the prediction accuracy for cryptocurrency prices can be significantly improved. However, the existing “decomposition–ensemble” systems decompose the entire financial data sample before splitting it into training and test sets, leading to potential data leakage, as the training set may already include information from the test set \[[29](https://www.mdpi.com/2504-3110/10/4/218#B29-fractalfract-10-00218)\].
As a data preprocessing and feature extraction method, Empirical Mode Decomposition (EMD) still demonstrates its unique superiority in many complex time series prediction tasks. When combined with deep learning models such as LSTM, EMD not only enhances the interpretability of data but also optimizes the prediction accuracy of the model, especially in the fields of stock market prediction, seasonality, and chaotic time series analysis \[[1](https://www.mdpi.com/2504-3110/10/4/218#B1-fractalfract-10-00218),[30](https://www.mdpi.com/2504-3110/10/4/218#B30-fractalfract-10-00218),[31](https://www.mdpi.com/2504-3110/10/4/218#B31-fractalfract-10-00218)\]. Compared to alternative decomposition methods such as VMD and Wavelet Transform, EMD is fully data-driven and requires no prior assumptions, making it particularly suitable for the adaptive, multi-scale analysis of non-stationary financial series. Its balance of interpretability, adaptability, and computational efficiency offers a distinct advantage in modeling complex cryptocurrency returns \[[32](https://www.mdpi.com/2504-3110/10/4/218#B32-fractalfract-10-00218)\]. Therefore, EMD still has irreplaceable advantages in improving prediction performance and robustness, especially when dealing with complex systems.
Building on previous research, this study explores a key issue: whether a sliding decomposition prediction method that overcomes data leakage can outperform the univariate system in predicting ADA returns. Additionally, we use the dynamic LASSO method to examine whether incorporating time-varying economic and policy factors can further enhance the prediction accuracy of ADA returns. These two aspects have often been overlooked in previous studies but are worth investigating \[[33](https://www.mdpi.com/2504-3110/10/4/218#B33-fractalfract-10-00218)\].
To address the limitations identified in prior research, this study introduces the following innovative improvements. First, to overcome the constraints of traditional econometric models in handling nonlinear and non-stationary series, as well as the inadequacy of machine learning methods in capturing the complex, chaotic nature of cryptocurrency markets, we adopt a decomposition–ensemble framework capable of adapting to multi-scale dynamics. Second, we propose a hybrid framework integrating sliding window EMD with machine learning. This approach eliminates the look-ahead bias inherent in full-sample decomposition, avoids the structural constraints of recurrent networks (e.g., LSTM, GRU) on non-stationary series, and leverages the robustness and efficiency of models to deliver superior forecasting performance. Finally, by embedding LASSO-based dynamic factor selection into the prediction of distinct frequency components, we enhance the economic interpretability and forecasting accuracy of the model, thereby achieving a substantive methodological advancement over existing frameworks.
## 3\. Methodology
This section introduces the framework for the Univariate Prediction System, the Multivariate Prediction System, the “Sliding EMD” prediction system, and the “Sliding EMD–Multi Variables” prediction system. We employ a suite of established machine learning models for these forecasting tasks, including Linear Regression (LR), Support Vector Regression (SVR), Random Forest (RF), Gradient Boosting Regression (GBR), and Extreme Gradient Boosting (XGB). These models were selected for their proven efficacy and computational efficiency in financial forecasting. While deep learning architectures can capture complex patterns, they often demand substantial computational resources, are prone to overfitting and output instability in high-frequency financial data, and may not consistently outperform well-tuned traditional machine learning models in return prediction tasks. In contrast, the chosen ensemble and kernel-based methods provide a robust balance between predictive power, interpretability, and training efficiency, and have been widely validated in prior cryptocurrency and financial time series forecasting studies \[[34](https://www.mdpi.com/2504-3110/10/4/218#B34-fractalfract-10-00218)\]. Additionally, [Appendix A.1](https://www.mdpi.com/2504-3110/10/4/218#secAdot1-fractalfract-10-00218), [Appendix A.2](https://www.mdpi.com/2504-3110/10/4/218#secAdot2-fractalfract-10-00218) and [Appendix A.3](https://www.mdpi.com/2504-3110/10/4/218#secAdot3-fractalfract-10-00218) provides detailed descriptions of the error metrics for prediction comparisons and the performance metrics for investment evaluation.
### 3\.1. Univariate Prediction System
The modeling process for the univariate system is shown in [Figure 1](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-f001). First, a fixed window is set, and the BIC criterion is used to select the optimal lag period. The ADA returns for the corresponding lag period are taken as the univariate input, and the future ADA returns are set as the target variable for fitting. For example, with a fixed window of 800 and an optimal lag period of 2, the training set inputs include data from periods 1 and 2, 2 and 3,…, 798 and 799, and the corresponding training set outputs are 3, 4,…, 800. The model is trained using these input–output pairs. For the test set, the ADA returns for periods 799 and 800 are used as input, and the trained model is used to predict the ADA returns for the 801st period.
![Fractalfract 10 00218 g001]()
**Figure 1.** The modeling process of the Univariate Prediction System. Note: [Figure 1](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-f001), [Figure 2](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-f002), [Figure 3](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-f003) and [Figure 4](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-f004) present the methodological workflow of the proposed forecasting systems and were created by the authors.
**Figure 1.** The modeling process of the Univariate Prediction System. Note: [Figure 1](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-f001), [Figure 2](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-f002), [Figure 3](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-f003) and [Figure 4](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-f004) present the methodological workflow of the proposed forecasting systems and were created by the authors.
![Fractalfract 10 00218 g001]()
![Fractalfract 10 00218 g002]()
**Figure 2.** The modeling process of the Multivariate Prediction System.
**Figure 2.** The modeling process of the Multivariate Prediction System.
![Fractalfract 10 00218 g002]()
![Fractalfract 10 00218 g003]()
**Figure 3.** The modeling process of the “Sliding EMD” system.
**Figure 3.** The modeling process of the “Sliding EMD” system.
![Fractalfract 10 00218 g003]()
![Fractalfract 10 00218 g004]()
**Figure 4.** The modeling process of the “Sliding EMD–Multi Variables” system.
**Figure 4.** The modeling process of the “Sliding EMD–Multi Variables” system.
![Fractalfract 10 00218 g004]()
[Figure A1](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-f0A1), [Figure A2](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-f0A2), [Figure A3](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-f0A3) and [Figure A4](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-f0A4) display the optimal hyperparameters for XGB, SVR, GBR, and RF models over 1199 sliding windows. In the “Sklearn” framework, dynamic hyperparameter selection is performed via grid search for each 800-period window. The results show that, for SVR, the parameter “C” is mainly 0.1, with some instances at 10. For XGB, the “maximum\_depth” is typically 3, with smaller portions at 5 and 7, while the “learning\_rate” is mainly 0.01. For GBR, the “maximum\_depth” is mostly 3, with some at 5 and 7, and the “learning\_rate” is 0.01. For RF, the “min\_samples\_split” is distributed across \[[3](https://www.mdpi.com/2504-3110/10/4/218#B3-fractalfract-10-00218),[5](https://www.mdpi.com/2504-3110/10/4/218#B5-fractalfract-10-00218),[7](https://www.mdpi.com/2504-3110/10/4/218#B7-fractalfract-10-00218)\], and the “maximum\_depth” is mostly 3, with smaller portions at 5 and 7.
### 3\.2. Multivariate Prediction System
The modeling process for the multivariate system is shown in [Figure 2](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-f002). The construction of this system is based on the univariate system, where relevant variables affecting ADA returns are selected for each sliding window. The LASSO method is used for feature selection from seven major categories of variables: macroeconomic variables, social variables, exchange rate variables, competitive variables, financial variables, commodity variables, and policy variables. The regularization parameter
λ
in LASSO is determined within each window via time series cross-validation, which preserves temporal ordering and selects the value that minimizes the one-step-ahead forecast error on the training segment. Variables with non-zero coefficients are retained, and variables with a LASSO coefficient of 0 are discarded. Then, the fixed window is moved forward by one step, and the LASSO selection is repeated for each window until the prediction is completed. The setting of the sliding window approach can help identify the time-varying characteristics of the impact of these seven variables on ADA returns. Furthermore, the LASSO selection results are incorporated as covariates into the prediction model, which improves prediction efficiency by integrating the economically significant variables, thereby improving prediction accuracy. [Figure A5](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-f0A5), [Figure A6](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-f0A6), [Figure A7](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-f0A7) and [Figure A8](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-f0A8) show the optimal hyperparameters for XGB, SVR, GBR, and RF models applied to the multivariate sliding window over 1199 windows.
### 3\.3. “Sliding EMD” System
The modeling process for the “Sliding EMD” prediction system is shown in [Figure 3](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-f003). For an 800-day fixed window, ADA returns are decomposed using the EMD algorithm into multiple modal components. These components are then adaptively grouped into high-frequency and low-frequency clusters via K-means clustering, which operates on a feature vector comprising the sample entropy of each component. This unsupervised clustering naturally separates components with a higher sample entropy into the high-frequency group and those with a lower sample entropy into the low-frequency group, based on the intrinsic complexity of their temporal patterns. This two-scale separation is grounded in the multi-scale nature of financial markets: high-frequency components capture short-term noise and transient shocks, while low-frequency components reflect long-term trends and persistent economic forces \[[35](https://www.mdpi.com/2504-3110/10/4/218#B35-fractalfract-10-00218)\]. Grouping components into these two distinct regimes allows the model to tailor predictive strategies to different temporal dynamics, thereby enhancing interpretability and forecast accuracy. The BIC criterion is applied to select the optimal lag periods for both components. Predictions for each component are summed to obtain the ADA returns for the 801st day. The window then slides forward, and the EMD and K-means reconstruction process is repeated until predictions are completed. The “Sliding EMD” system addresses data leakage issues seen in previous studies, and K-means clustering offers low computational cost with effective reconstruction results. The high-frequency and low-frequency components can also incorporate additional variables. For machine learning methods, optimal parameter tuning is required for both components. To ensure no future information is used, hyperparameter selection is performed independently within each rolling window: a grid search is conducted on the in-sample data of the current window using walk-forward validation, and the best-performing set is retained to forecast the next out-of-sample point. This process yields two sets of dynamic hyperparameters, one for the high-frequency and one for the low-frequency component, that adapt to local market patterns. [Figure A9](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-f0A9), [Figure A10](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-f0A10), [Figure A11](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-f0A11), [Figure A12](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-f0A12), [Figure A13](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-f0A13), [Figure A14](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-f0A14), [Figure A15](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-f0A15) and [Figure A16](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-f0A16) display these dynamically selected optimal hyperparameters for the XGB, SVR, GBR, and RF models applied to the high-frequency and low-frequency components.
### 3\.4. “Sliding EMD–Multi Variables” System
Building on the “Sliding EMD” framework, the “Sliding EMD–Multi Variables” prediction system incorporates LASSO dynamic factor selection for the high-frequency and low-frequency components obtained from each fixed window decomposition. This allows for information gain at the frequency component level, as shown in [Figure 4](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-f004). After component decomposition, reconstruction, and BIC optimal lag selection within each window, LASSO factor selection is applied to identify economic factors influencing ADA returns. The selected factors and optimal lag periods for each component are then used to predict the future values of both frequency components.
For a fixed window of 800, the ADA returns from periods 1 to 800 are decomposed using EMD, and the high-frequency and low-frequency components are reconstructed using K-means. The lag periods for each component are used for fitting, followed by the LASSO selection of key variables with non-zero coefficients for prediction. The predicted values for both components on the 801st day are then summed to obtain the predicted ADA returns. The window is then moved forward by one step, and the process is repeated. [Figure A17](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-f0A17), [Figure A18](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-f0A18), [Figure A19](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-f0A19), [Figure A20](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-f0A20), [Figure A21](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-f0A21), [Figure A22](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-f0A22), [Figure A23](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-f0A23) and [Figure A24](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-f0A24) show the dynamic optimal hyperparameters for XGB, SVR, GBR, and RF models applied to these components.
## 4\. Data Description
### 4\.1. ADA Price and Returns
The ADA return data cover the period from 13 July 2019 to 31 December 2024. Data frequency is daily, and the total data size is 1999.This period includes significant events such as the U.S.–China trade war, fluctuations in commodity prices, the COVID-19 pandemic, and geopolitical conflicts, which provide support for validating the stability of the forecasting system proposed in this study. All subsequent return calculations are based on the logarithmic difference method, which is formulated as follows:
y
t
\=
ln
P
t
/
P
t
−
1
(1)
[Figure 5](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-f005) shows the daily closing price and return series of ADA (data source: <https://cn.investing.com/crypto/cardano/historical-data>, accessed on 26 January 2026). Before 2021, ADA’s technological development was limited, and its price remained low. In September 2021, a significant upgrade introduced smart contract functionality, attracting investor attention. This coincided with a global cryptocurrency bull market, pushing ADA’s price to a peak of \$3\.10. In 2022, macroeconomic tightening and industry crises caused a 60% market cap reduction, leading ADA’s price to fall to \$0\.25 by year-end, a 92% drop from its peak. In 2023, ADA introduced new technology and partnerships, but U.S. regulatory scrutiny hindered price growth. By 2024, with the approval of cryptocurrency-related financial products (spot ETFs), market confidence returned, and ADA’s price slightly rebounded to \$0\.70.
Historical data show that ADA’s price is susceptible to technological upgrades and industry events. Its high volatility is driven by both technological potential and the inherent risk of the cryptocurrency market. The return series highlights frequent, large fluctuations, indicating a significant uncertainty in ADA’s daily returns. This volatility persists, reflecting the ongoing high risk.
### 4\.2. Seven Key Factors Influencing ADA
This study identifies seven key factors: macroeconomic, financial, commodity, exchange rate, policy, attention, and competition variables. Based on Corbet et al. (2020) \[[36](https://www.mdpi.com/2504-3110/10/4/218#B36-fractalfract-10-00218)\], macroeconomic variables include the U.S. federal funds rate, CPI, unemployment rate, and the global Economic Policy Uncertainty index. Financial variables, as suggested by Sánchez et al. (2024) \[[37](https://www.mdpi.com/2504-3110/10/4/218#B37-fractalfract-10-00218)\], include the S\&P 500, NASDAQ, and VIX indices. Commodity variables, such as metal and energy prices, affect ADA based on Manavi et al. (2020) \[[38](https://www.mdpi.com/2504-3110/10/4/218#B38-fractalfract-10-00218)\], with the CRB index representing commodity market influence. Exchange rate fluctuations like USD/CNY and USD/EUR relate to cryptocurrency volatility, prompting a focus on the exchange rate’s role in predictions. According to Isah et al. (2019) \[[39](https://www.mdpi.com/2504-3110/10/4/218#B39-fractalfract-10-00218)\], policy variables such as U.S. fiscal and monetary policy indices significantly impact ADA. Following Auer et al. (2022) \[[40](https://www.mdpi.com/2504-3110/10/4/218#B40-fractalfract-10-00218)\], the Google search index for key ADA events is used as a measure of attention, with 42 key events tested using Granger causality and synthesized via the GDFM model. The competition variable considers Bitcoin and Ethereum, as De et al. (2023) \[[41](https://www.mdpi.com/2504-3110/10/4/218#B41-fractalfract-10-00218)\] found a competitive relationship among major cryptocurrencies. [Figure 6](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-f006) presents the four outcomes of the subsequent LASSO screening: the NASDAQ Composite Index, S\&P 500 Index, US Monetary Policy Index, and US Fiscal Policy Index.
Exchange rates for USD/CNY, USD/EUR, the S\&P 500, VIX, NASDAQ, federal funds rate, U.S. CPI, and U.S. unemployment data are sourced from the Federal Reserve Economic Data (FRED) website: <https://fred.stlouisfed.org/>, accessed on 26 January 2026. CRB, Bitcoin, and Ethereum data come from the Choice Financial Terminal. The global EPU index, U.S. fiscal policy index, and U.S. monetary policy index are directly downloaded from <https://www.policyuncertainty.com/>, accessed on 26 January 2026.
To ensure temporal consistency and prevent the use of future information, all lower-frequency variables are manually aligned with the daily ADA return series. Specifically, for a given month, the same monthly value is assigned to every trading day within that month. This alignment preserves the chronological order of information and eliminates look-ahead bias, as only data available up to each prediction point are used in the rolling window forecasting process.
### 4\.3. Factor Selection Results Based on Least Absolute Shrinkage and Selection Operator (LASSO)
#### 4\.3.1. Factors in the Multivariate Prediction System
In the multivariate sliding window prediction system described in the methodology section, the LASSO method dynamically selects factors from the seven key variables within each sliding window. Since this system performs less effectively than the “Sliding EMD–Multi Variables” prediction system, only a brief introduction to the factor selection results is provided. [Figure A25](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-f0A25) shows the LASSO dynamic factor selection results. It reveals that, without decomposition, the NASDAQ index is selected in nearly all windows, highlighting its substantial impact on ADA returns. The S\&P 500 is chosen in all windows until June 2023, indicating its comparable predictive importance. The U.S. monetary policy variable mainly contributes between October 2021 and May 2022, and in November 2024. [Figure A26](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-f0A26), [Figure A27](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-f0A27) and [Figure A28](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-f0A28) show the dynamic coefficient plots of the LASSO-selected variables for each window in the multivariate system.
#### 4\.3.2. Factors in the “Sliding EMD–Multi Variables” Prediction System
[Figure 7](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-f007) shows the LASSO dynamic factor selection results for the high-frequency components in the “Sliding EMD–Multi Variables” prediction system. Under the sliding window decomposition, the NASDAQ variable is selected in every window, and the S\&P 500 is frequently selected until June 2023. U.S. monetary policy impacts the high-frequency component, especially before April 2022 and after November 2024, consistent with the multivariate sliding window results. U.S. fiscal policy affects the high-frequency component intermittently in 2021 and 2022. The coefficients for the NASDAQ and S\&P 500 are inversely related: NASDAQ has a positive impact, while the S\&P 500 has a negative one. Fiscal and monetary policy variables mainly have a negative impact, except for monetary policy in 2024, which has a positive effect.
[Figure 8](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-f008) shows the dynamic coefficient plots for the high-frequency factors in the “Sliding EMD–Multi Variables” prediction system. From September 2021 to January 2022, the NASDAQ coefficient is positively correlated with ADA, as the Federal Reserve reduced bond purchases, causing volatility in NASDAQ stocks and increasing the short-term correlation with ADA. During the same period, the S\&P 500 coefficient fluctuates negatively, indicating a weakening correlation with ADA due to concerns about economic recession and a shift away from traditional industries. Monetary policy coefficients show a negative relationship with ADA, reflecting the impact of expected interest rate hikes, which led funds to flow into the U.S. dollar and Treasury bonds.
From May 2022, the NASDAQ coefficient turned negative, while the S\&P 500 coefficient shifted positive, reflecting a decline in technology stock valuations and a rise in traditional industries, which led to a drop in ADA’s price. From January to May 2023, both coefficients are significantly negative due to the Silicon Valley Bank incident, which heightened concerns about financial stability. After May 2023, the NASDAQ coefficient turns slightly positive, reflecting a shift in U.S. Federal Reserve policy and easing expectations, driving both the Nasdaq index and ADA higher. In the second half of 2024, the monetary policy coefficient turns positive as the Federal Reserve signals interest rate cuts due to declining inflation expectations, prompting capital inflows into the cryptocurrency market.
The high-frequency model captures short-term shocks to the ADA market. As a barometer for tech stocks, NASDAQ’s volatility reflects market risk appetite and liquidity expectations, making ADA returns highly sensitive to tech sector sentiment. The S\&P 500’s short-term fluctuations mirror macroeconomic risks and industry volatility, acting as a haven during systemic risk and returning to a risk asset status during liquidity expansion. The persistent negative fiscal policy coefficient reflects the impact of short-term fiscal funds and regulatory risks on ADA, while the dynamic monetary policy coefficient captures shifts in short-term liquidity cycles from tightening to easing.
[Figure 9](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-f009) shows the LASSO dynamic factor selection results for the low-frequency components in the “Sliding EMD–Multi Variables” prediction system. The NASDAQ variable is selected throughout, and the S\&P 500 is frequently selected until June 2023, consistent with the high-frequency results. The factors for the low-frequency components align with those for high-frequency components, with NASDAQ having a positive impact and the S\&P 500 having a negative impact.
[Figure 10](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-f010) shows the dynamic coefficient plots for the low-frequency factors in the “Sliding EMD–Multi Variables” prediction system. From September 2021 to January 2022, the NASDAQ coefficient was significantly positive and linked to the ADA contract technology upgrade. In May 2022, it briefly dropped due to a reduced correlation between tech stocks and cryptocurrencies from interest rate hikes. From September 2022 to early 2023, the coefficient continues to decline. After 2023, the NASDAQ coefficient becomes persistently positive but with a smaller magnitude, indicating a weakening long-term correlation with traditional markets.
The impact of the S\&P 500 on the low-frequency component of ADA returns is more pronounced. From 2021 to 2023, the S\&P 500 coefficient remains significant and negative, but after 2023 it becomes zero, indicating no further impact on ADA returns. As a diversified market index, the S\&P 500 reflects a long-term driving factor that differs from ADA, with the coefficient showing a negative correlation between traditional industries and ADA.
The low-frequency model captures long-term market linkages, with policy shocks transmitted through market indices rather than policy variables. The common trend between U.S. tech stocks and ADA remains stable across cycles. The low-frequency data highlights ADA’s independence from traditional indices, filtering out short-term fluctuations and emphasizing the role of technology and macro events on the NASDAQ coefficient. The negative S\&P 500 coefficient reflects the disconnect between the traditional economy and the cryptocurrency market, showing no correlation or a negative one with traditional economic cycles.
After sliding window decomposition, financial variables have the most significant influence. Policy variables impact high-frequency components but not low-frequency components. Compared to the non-decomposed system, fiscal policy significantly affects ADA after EMD. The high-frequency model focuses on short-term dynamics, while the low-frequency model captures long-term trends in market indices. These variable selections reflect the heterogeneous driving factors across time scales.
## 5\. Empirical Results
This section consists of prediction results, investment results, MCS (Model Confidence Set) tests, and comparisons between the univariate system (System 1), multivariate system (System 2), “Sliding EMD” system (System 3), and “Sliding EMD–Multi Variables” system (System 4). The prediction metrics used include MSE, RMSE, MAE, SMAPE, and DSTAT, which represent the performance of different prediction system models. When predicting ADA returns, it is crucial to emphasize practical applicability, especially the impact on investment decisions. For investment results, metrics such as the average daily returns, maximum drawdown, Sharpe ratio, Sortino ratio, and Calmar ratio are used to evaluate the investment performance changes across different systems. Finally, to comprehensively assess the overall effectiveness of the prediction systems, the MCS test is more appropriate. Therefore, the MCS test is used further to verify the advantages and disadvantages of the four systems. [Table A1](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-t0A1) provides the Univariate Prediction System prediction results, [Section 5.1](https://www.mdpi.com/2504-3110/10/4/218#sec5dot1-fractalfract-10-00218) presents the forecasting results and investment performance of the Multivariate Prediction System, [Section 5.2](https://www.mdpi.com/2504-3110/10/4/218#sec5dot2-fractalfract-10-00218) presents the “Sliding EMD” system prediction results and investment comparison, and [Section 5.3](https://www.mdpi.com/2504-3110/10/4/218#sec5dot3-fractalfract-10-00218) presents the “Sliding EMD–Multi Variables” system prediction results and investment comparison.
### 5\.1. Prediction Results for the Multivariate Prediction System
In the Multivariate Prediction System, the LASSO method is applied to the raw ADA returns series to select dynamic factors with non-zero coefficients for prediction. [Table 1](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-t001) shows the prediction results for the five models under the multivariate, and [Table 2](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-t002) presents the comparison between the Multivariate Prediction System and the Univariate Prediction System. The values in [Table 2](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-t002) represent changes relative to the Univariate Prediction System, where a “–” indicates worse forecast performance and a “+” indicates better forecast performance. It can be seen that, aside from four error metrics in the GBR and XGB models where the Multivariate Prediction System performs better, all other model performances are worse. On average, the five models in the Multivariate Prediction System have worsened by 5.422%, 2.614%, 2.972%, 0.572%, and 13.226% in terms of MSE, RMSE, MAE, SMAPE, and DSTAT, respectively. Therefore, under the Multivariate Prediction System, when decomposition techniques are not used, the performance and investment efficiency after incorporating predictive variables are inferior to those of the Univariate Prediction System. The MCS test results in [Table A2](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-t0A2) also indicate that the Multivariate Prediction System performs worse.
### 5\.2. Prediction Results for the “Sliding EMD” System
In the “Sliding EMD” prediction system, a sliding window EMD, K-means clustering, and five prediction methods are applied, focusing on the multi-scale modal features of ADA returns data.
[Table 3](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-t003) shows the prediction results for the five models under the “Sliding EMD” System. The MSE, RMSE, MAE, SMAPE, and DSTAT for the LR model are 3.53 × 10−4, 0.0188, 0.0134, 1.64, and 0.510, respectively. [Figure 11](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-f011) shows the comparison of this system with the Univariate Prediction System. The closer the comparison index of the radar chart is to the external circle, the better the improvement of the system will be. Assuming the prediction models remain unchanged, except for LR (MAE), XGB (MAE), GBR (MAE), and RF (DSTAT), the error metrics improve due to the sliding window decomposition technique. For instance, compared to System 1, the LR model improved MSE by 0.16%, RMSE by 0.08%, MAE by 0.42%, and SMAPE by 4.65%, and DSTAT remained unchanged. On average, the system improved by 0.828% for MSE, 0.416% for RMSE, 5.234% for SMAPE, and 0.418% for DSTAT.
[Figure 12](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-f012) compares the “Sliding EMD” system with the Multivariate Prediction System. Assuming the prediction models remain unchanged, except for XGB (MAE) and GBR (MSE, MAE), the decomposition technique in this system outperforms the Multivariate Prediction System for all other error metrics. For example, compared to System 2, the LR model improved MSE by 12.77%, RMSE by 6.60%, MAE by 7.23%, SMAPE by 5.62%, and DSTAT by 33.81%. On average, the five models improved by 5.522% for MSE, 3.144% for RMSE, 2.602% for MAE, 5.746% for SMAPE, and 17.616% for DSTAT.
![Fractalfract 10 00218 g012]()
**Figure 12.** Comparison of prediction accuracy between the “Sliding EMD” system and the Multivariate Prediction System. Note: [Figure 11](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-f011), [Figure 12](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-f012), [Figure 13](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-f013) and [Figure 14](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-f014) are plotted by the authors based on the empirical results of this study.
**Figure 12.** Comparison of prediction accuracy between the “Sliding EMD” system and the Multivariate Prediction System. Note: [Figure 11](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-f011), [Figure 12](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-f012), [Figure 13](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-f013) and [Figure 14](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-f014) are plotted by the authors based on the empirical results of this study.
![Fractalfract 10 00218 g012]()
![Fractalfract 10 00218 g013]()
**Figure 13.** Comparison of prediction accuracy between the “Sliding EMD–Multi Variables” system and the “Sliding EMD” system. Note: The radar chart also shows percentage data. The closer to the center of the origin, the smaller the data becomes. The further out the data, the greater the percentage, and the stronger the improvement percentage in the comparison between the two systems.
**Figure 13.** Comparison of prediction accuracy between the “Sliding EMD–Multi Variables” system and the “Sliding EMD” system. Note: The radar chart also shows percentage data. The closer to the center of the origin, the smaller the data becomes. The further out the data, the greater the percentage, and the stronger the improvement percentage in the comparison between the two systems.
![Fractalfract 10 00218 g013]()
![Fractalfract 10 00218 g014]()
**Figure 14.** Daily return comparison for the “Sliding EMD–Multi Variables” system.
**Figure 14.** Daily return comparison for the “Sliding EMD–Multi Variables” system.
![Fractalfract 10 00218 g014]()
The MCS test in [Table 4](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-t004) shows that, when comparing System 3 with System 1, the univariate SVR is the worst, while the LR model in the “Sliding EMD” system performs the best. System 3 has an average ranking of 4.2, compared to 6.8 for System 1. When comparing System 3 with System 2, the SVR model under the Multivariate Prediction System performs the worst, and the GBR model under the Multivariate Prediction System performs the best. System 3 has an average ranking of 4.6, while System 2 has an average ranking of 6.2. Overall, System 3 outperforms both System 1 and System 2, which is consistent with the error metric results. The pure decomposition system outperforms both the non-decomposed and multivariate added prediction systems, proving the full effectiveness of decomposition techniques in ADA prediction.
Additionally, this study compares investment performance across the “Sliding EMD” system, the Multivariate Prediction System, and the Univariate Prediction System. [Table 5](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-t005) presents the daily return comparisons. Compared with System 1, System 3’s models show the following improvements in daily return: LR by 9.00 × 10−5, GBR by 3.63 × 10−4, RF by 5.74 × 10−4, SVR by 2.50 × 10−4, and XGB by 5.43 × 10−4. Compared with System 2, System 3’s models improve by 2.64 × 10−3 (LR), 3.76 × 10−4 (GBR), 1.35 × 10−3 (RF), 2.27 × 10−3 (SVR), and 4.24 × 10−4 (XGB). Overall, System 3 outperforms System 1 by an average of 3.64 × 10−4 and System 2 by an average of 1.412 × 10−3 in daily returns. [Table A3](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-t0A3), [Table A4](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-t0A4), [Table A5](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-t0A5) and [Table A6](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-t0A6) illustrate comparisons of the maximum drawdown ratio, Sharpe ratio, Sortino ratio, and Calmar ratio.
### 5\.3. Prediction Results for the “Sliding EMD–Multi Variables” System
In the “Sliding EMD–Multi Variables” prediction system, this study builds upon the “Sliding EMD” system’s decomposition and reconstruction framework. For each fixed window, the high-frequency and low-frequency components obtained through reconstruction are combined with the non-zero coefficient factors selected by the LASSO model as covariates to assist in prediction. [Table 6](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-t006) shows the prediction results for the five models under this system. [Figure 13](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-f013) compares the results with System 3. For the LR model, the MSE improves by 0.94%, RMSE improves by 0.47%, MAE improves by 0.78%, SMAPE worsens by 2.62%, and DSTAT worsens by 0.73%. In the MSE metric, all models perform better, with an average improvement of 0.687%. The RMSE metric also improves on average by 0.338%. The MAE metric is seen as a disadvantage in GBR and XGB, but the other models show an average improvement of 0.266%. The SMAPE and DSTAT metrics do not surpass System 3. The above analysis indicates that incorporating economic variables into the frequency components in the “Sliding EMD–Multi Variables” system improves ADA return forecasting accuracy compared to the “Sliding EMD” system, albeit by a small margin.
[Figure A29](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-f0A29) shows the comparison with the Multivariate Prediction System. For the LR model, MSE improves by 13.59%, RMSE improves by 7.04%, MAE improves by 7.95%, SMAPE improves by 3.15%, and DSTAT improves by 32.82%. Decomposition technology brings significant improvements to all metrics, with the exception of GBR, which sees a slight decline. On average, the five models show improvements of 6.136% for MSE, 3.174% for RMSE, 2.844% for MAE, 3.154% for SMAPE, and 17.528% for DSTAT.
[Figure A30](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-f0A30) compares the ADA return prediction with the Univariate Prediction System. For the LR model, MSE improves by 1.10%, RMSE improves by 0.55%, MAE improves by 0.36%, SMAPE improves by 2.03%, and DSTAT worsens by 14.06%. Decomposition and multivariate inclusion lead to a slight deterioration in DSTAT, GBR (MAE), SVR (SMAPE), and XGB (MAE), while other models show improvements in MSE, RMSE, MAE, and SMAPE, with average improvements of 1.506% for MSE, 0.754% for RMSE, 0.13% for MAE, and 2.478% for SMAPE.
The MCS test results for System 4 are shown in [Table 7](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-t007). When comparing System 4 with System 1, the SVR model in the univariate system performs the worst, while the LR model in the “Sliding EMD” system performs the best. System 4 has an average ranking of 7, compared to 4 for System 1. When comparing System 4 with System 2, the SVR model in the multivariate system performs the worst, and the LR model performs the best. System 4 has an average ranking of 4.4, while System 2 has an average ranking of 6.6. When comparing System 4 with System 3, the SVR model under the “Sliding EMD” framework performs the worst, and the LR model under the “Sliding EMD–Multi Variables” framework performs the best. System 4 has an average ranking of 5.4, while System 3 has an average ranking of 5.6.
In the investment performance comparison for System 4, [Figure 14](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-f014) shows the daily return metrics. Compared to System 1, except for the LR model, all models in System 4 perform better. The LR model worsens by 2.55 × 10−4, while GBR improves by 1.74 × 10−4, RF improves by 6.32 × 10−4, SVR improves by 4.14 × 10−4, and XGB improves by 2.86 × 10−4, with an average improvement of 2.502 × 10−4. System 4 performs better than System 2 across all five models, with LR improving by 2.29 × 10−3, GBR improving by 1.87 × 10−4, RF improving by 1.41 × 10−3, SVR improving by 2.44 × 10−3, and XGB improving by 1.67 × 10−4, with an average improvement of 1.2988 × 10−3. However, System 4 lags behind System 3, with only RF and SVR improving by 5.80 × 10−5 and 1.64 × 10−4, respectively, resulting in an average decrease of 1.138 × 10−4. [Table A7](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-t0A7), [Table A8](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-t0A8), [Table A9](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-t0A9) and [Table A10](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-t0A10) present the comparisons for the maximum drawdown ratio, Sharpe ratio, Sortino ratio, and Calmar ratio. In terms of the maximum drawdown ratio, System 4 improves by an average of 0.166 compared to System 1, and by an average of 0.439 compared to System 2. For the Sharpe ratio, System 4 improves by an average of 0.114 compared to System 1, and by an average of 1.549 compared to System 2. The Sortino ratio shows an improvement of 0.560 for System 4 compared to System 1, and 3.876 compared to System 2. In the Calmar ratio, System 4 improves by an average of 0.0802 compared to System 1, and by 0.239 compared to System 2.
Based on the overall prediction results, investment outcomes, and MCS tests, the Multivariate Prediction System is inferior to the univariate system, the “Sliding EMD” system outperforms both the Univariate and Multivariate Prediction Systems, and the “Sliding EMD–Multi Variables” system does not show a significant improvement over the “Sliding EMD” system but significantly outperforms both the multivariate and univariate systems.
The advantage of the “Sliding EMD” system highlights the importance of the multi-scale composite system method combining the sliding window EMD and K-means clustering proposed in this study. EMD decomposes the complex ADA return series into components at multiple scales via multi-scale analysis, while the sliding window approach effectively prevents the data leakage inherent in traditional decomposition algorithms and ensures that each prediction step is based on real-time information. K-means clustering then adaptively reorganizes these components within each fixed window into high-frequency and low-frequency elements, enhancing prediction accuracy and enabling the subsequent inclusion of variable effects. System 3 significantly outperforms both the univariate and multivariate systems in prediction accuracy and investment performance, demonstrating that the combination of EMD and K-means clustering can effectively extract insights from the ADA time series and provide more reliable support for investment decisions. [Section 4.3.2](https://www.mdpi.com/2504-3110/10/4/218#sec4dot3dot2-fractalfract-10-00218) identified that U.S. stock market, U.S. fiscal policy, and U.S. monetary policy significantly affect different frequency components of ADA returns. The empirical results also show that the “Sliding EMD–Multi Variables” system delivers a slight improvement in forecasting accuracy compared to the “Sliding EMD” system, demonstrating the impact of these key economic variables.
## 6\. Discussion of ADA Return Prediction Results
In recent years, many studies have combined machine learning with the multi-factor prediction of financial asset prices. However, current studies using decomposition algorithms have data leakage problems, and few use real investment performance to verify the model’s application value. [Table 8](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-t008) compares these studies regarding sliding windows, variables, models, etc.
This section compares the “Sliding EMD–Multi Variables” framework with existing forecasting methods. A key question is whether the sliding window decomposition is better than the traditional univariate decomposition. Xu and Niu (2023) \[[13](https://www.mdpi.com/2504-3110/10/4/218#B13-fractalfract-10-00218)\] found that the multi-step sliding window decomposition has a greater prediction advantage for oil price forecasting than the single-step one. However, the sliding decomposition is still not better than the traditional univariate forecast. Although the sliding window method can prevent data leakage, it also reduces the forecast accuracy. However, these studies rarely apply sliding window decomposition to ADA returns. Our results based on error indicators and MCS tests show that the “Sliding EMD” framework outperforms the traditional Univariate Prediction System in ADA return forecasting. Our research offers practical insights into whether including economic and financial variables improves ADA prediction and elucidates whether decomposition techniques and factor selection can further enhance forecasting accuracy.
The existing decomposition forecasting studies, such as those by Viéitez et al. (2024) \[[29](https://www.mdpi.com/2504-3110/10/4/218#B29-fractalfract-10-00218)\], Buse et al. (2025) \[[43](https://www.mdpi.com/2504-3110/10/4/218#B43-fractalfract-10-00218)\], and Li et al. (2022) \[[28](https://www.mdpi.com/2504-3110/10/4/218#B28-fractalfract-10-00218)\], mainly focus on applying advanced single machine learning algorithms or combined models to different decomposed components to obtain comparative advantages but ignore the impact of combining important economic and financial variables, that is, enhancing forecasts through data-driven approaches. However, studies by Bouri et al. (2021) \[[7](https://www.mdpi.com/2504-3110/10/4/218#B7-fractalfract-10-00218)\], Jiang et al. (2021) \[[15](https://www.mdpi.com/2504-3110/10/4/218#B15-fractalfract-10-00218)\], and Hajek et al. (2023) \[[42](https://www.mdpi.com/2504-3110/10/4/218#B42-fractalfract-10-00218)\] show that macroeconomic indicators, exchange rates, financial markets, commodities, monetary and fiscal policies, and online attention all significantly affect ADA returns. Including these variables can improve forecast accuracy, but few studies do so. In this study, based on the “Sliding EMD” framework, we use the LASSO method to screen factors that affect different frequency domain components of ADA returns within each fixed window and then incorporate these selected factors into the forecasting process. Compared with the “Sliding EMD” system, the “Sliding EMD–Multi Variables” system, which is constructed this way, further reduces the forecast error index. It improves investment performance through a data-driven approach and demonstrates the effectiveness of adding component-level variable effects in a sliding window decomposition framework. To date, ADA return forecasting studies have rarely examined the impact of economic and financial factors, especially within a sliding window decomposition framework. By doing so, our study provides practical insights into whether including economic and financial variables improves ADA forecasts and sheds light on whether decomposition techniques and factor selection can improve forecast accuracy.
Finally, these findings have significant practical value for policymakers, financial institutions, and investors. Policymakers can use the multi-scale composite framework developed in this paper as a macroprudential tool for the cryptocurrency market. For example, among the high-frequency components, US fiscal policy, US monetary policy, NASDAQ index, and S\&P 500 index, all affect ADA returns. Regulators can establish a real-time monitoring system to monitor changes in these economic variables to prevent excessive volatility in ADA prices. For investors, using the “Sliding EMD–Multi Variables” forecasting system can increase daily returns by 3.64 × 10−4 compared to the traditional Univariate Prediction System.
## 7\. Conclusions
The Sliding EMD method and economic variables are critical in predicting ADA coin returns. This study constructs four prediction frameworks to assess their effectiveness: the traditional Univariate Prediction System (System 1), the Multivariate Prediction System (System 2), the “Sliding EMD” prediction system (System 3), and the “Sliding EMD–Multi Variables” prediction system (System 4). The empirical results indicate the following:
(1) Regarding the interpretability of ADA return forecasting, financial and policy variables significantly impact both the original ADA return series and the frequency components extracted through Sliding EMD, exhibiting time-varying effects. U.S. fiscal and monetary policies only affect the high-frequency components, while financial variables such as the S\&P 500 and Nasdaq are significant drivers of both high- and low-frequency ADA returns.
(2) In terms of prediction performance, the constructed Multivariate Prediction System does not improve prediction performance. The “Sliding EMD “ prediction system and the “Sliding EMD–Multi Variables” prediction system frameworks demonstrate improvements over the traditional Univariate Prediction System. Specifically, System 3 improved MSE by 0.16%, RMSE by 0.08%, and SMAPE by 4.65%, with DSTAT being unchanged. System 4 follows closely, with improvements of 1.1% in MSE, 0.55% in RMSE, 0.36% in MAE, and 2.03% in SMAPE. These results indicate that Sliding EMD, combined with economic and financial driving variables at the component level, enhances the prediction of ADA returns.
(3) Based on the comparison of investment performance based on the prediction results, the daily return rate of System 3 is better than that of System 1. Similarly, the daily return rate of System 4 is also better than that of System 1. On average, the daily return rate of System 3 is 3.64 × 10−4 higher than that of System 1; the daily return rate of System 4 is 2.502 × 10−4 higher than that of System 1. These investment results are consistent with the prediction accuracy ranking, highlighting this study’s practical value.
This study innovatively applies sliding Empirical Mode Decomposition to predicting ADA returns. This method can decompose the original price series into intrinsic mode functions of different frequencies, effectively capturing information about different frequencies. At the same time, by correlating key economic and financial variables with varying components of frequency obtained using Sliding EMD, this study revealed for the first time that the impact of economic variables on ADA returns has a significant frequency dependence, and these impacts show time-varying characteristics. This provides a new perspective for understanding the complex driving mechanism of the cryptocurrency market.
The findings of this study have important practical significance and broad application prospects, especially for investors and traders, fund managers and quantitative teams, policymakers, and regulators in the cryptocurrency market. For investors and traders, the “Sliding EMD–Multi Variables” forecasting framework (System 4) provided by the study can be used as a core tool for building more accurate trading strategies. Its significantly improved forecasting accuracy directly translates into potential excess returns, which is of great value to active investors. For fund managers and quantitative teams, the study provides a ready-made forecasting tool (System 4), which reveals the frequency decomposition characteristics of the Cardano yield and its correlation mechanism with the macroeconomy. This provides a theoretical and empirical basis for fund managers to design quantitative strategies and conduct risk management. The improved forecasting accuracy directly translates into potential excess returns. This improvement is of great value to active investors. For policymakers and regulators, the study quantifies the significant impact of macroeconomic policies, especially U.S. fiscal and monetary policies, on the volatility of ADA returns from a short-term perspective. This helps policymakers provide decision-making references for formulating macroprudential regulatory frameworks and risk warning mechanisms.
Despite the current research’s findings, there are limitations and room for improvement in ADA return prediction. The K-means clustering method only divides the components into high-frequency and low-frequency categories. Clustering into more components may yield better results. As the research conclusions show, the machine learning models used in this study demonstrate a varying superiority across different prediction systems, and future research could explore using model averaging and weighted integration to combine the advantages of various models. This study examined the EMD algorithm but did not further test the effectiveness of other algorithms. Future research could explore decomposition algorithms with fixed component numbers (such as VMD and SSA), which remain potential areas for further study. Furthermore, the present framework was validated solely on ADA. Although ADA is a prominent and representative cryptocurrency, future work should extend the analysis to other major digital assets to assess the model’s generalizability across different market structures and volatility regimes.
## Author Contributions
W.Z.: Conceptualization, Formal analysis, Investigation; Z.T.: Formal analysis, Writing—original draft, Investigation; X.Z.: Formal analysis, Writing—original draft, Investigation; Y.C.: Data curation, Software, Writing—review and editing; B.D.: Software, Visualization, Validation. All authors have read and agreed to the published version of the manuscript.
## Funding
This research work was supported by the National Natural Science Foundation of China under Grant No. 72341030.
## Data Availability Statement
The original contributions presented in this study are included in the article and [Appendix A](https://www.mdpi.com/2504-3110/10/4/218#app1-fractalfract-10-00218). Further inquiries can be directed to the corresponding author.
## Conflicts of Interest
The authors declare no conflicts of interest.
## Appendix A
### Appendix A.1. Investment Strategy Design
The prediction results from the four systems discussed in the main text can be applied to the design of quantitative investment strategies and investment performance evaluation to assess the practical application value of the models. Since the prediction target in this project is ADA coin returns, which have directional characteristics, we assume investment in a related ADA coin index. Based on the model’s predictions of the index’s upward or downward movement (represented by 1 and 0), there are four trading scenarios: 0-0 represents no position, 0-1 represents entering a position, 1-0 represents closing a position, and 1-1 represents holding a position. The daily returns of each trading day are calculated to evaluate the investment performance of the four prediction systems.
### Appendix A.2. Evaluation Metrics
There are two categories of evaluation metrics: one for assessing prediction results and the other for the economic evaluation of investment performance. For prediction results, this study uses Mean Absolute Error (MAE), Mean Squared Error (MSE), Root Mean Squared Error (RMSE), Symmetric Mean Absolute Percentage Error (SMAPE), and the Directional Accuracy Statistic (DSTAT). The relevant formulas are shown in Equation (A1). Here, T represents the number of samples in the test set,
y
t
is the true value at time t,
y
^
t
is the predicted value at time t, and
I
(
)
is an indicator function that takes the value of 1 when the condition is met; otherwise, it takes the value of 0. The economic evaluation metrics for investment performance include the average daily return, maximum drawdown, Sharpe ratio, Sortino ratio, and Calmar ratio. The formulas for calculating the maximum drawdown, Sharpe ratio, Sortino ratio, and Calmar ratio are shown in Equation (A2). In these formulas,
E
r
p
represents the expected return of the asset,
r
f
is the risk-free rate,
σ
p
is the asset volatility,
R
p
,
t
is the sample return below the risk-free rate, and
D
i
and
D
j
are the asset net values at different times.
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The reason for selecting the above metrics to evaluate investment performance is as follows: the average daily return reflects the short-term profitability of the investment portfolio, making it easy to compare different strategies; the maximum drawdown reflects the maximum loss from peak to trough during a specific period, serving as an important risk measure for the strategy; the Sharpe ratio measures the excess returns per unit of total risk (including volatility), which is a classic metric for evaluating risk-adjusted returns; the Sortino ratio considers only downside risk, making it more suitable for assessing the investor’s sensitivity to losses; the Calmar ratio measures the excess returns per unit of maximum drawdown and is useful for evaluating long-term investment strategies’ risk-adjusted returns.
### Appendix A.3. Model Confidence Set Test
This research utilizes the Model Confidence Set (MCS) test to evaluate and compare the predictive performance of multiple models within two forecasting systems.
Assume the candidate model set constitutes
M
0
. The purpose of the MCS test is to identify the Model Confidence Set
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1
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∗
.
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includes all the best models at the confidence level
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M
. This elimination process will continue until the null hypothesis
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is no longer rejected at the confidence level
α
. At this point, the remaining models constitute the Model Confidence Set
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∗
. If the confidence level
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remains unchanged during each step of the elimination process, then
M
1
−
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∗
includes the best prediction models based on the
1
−
α
confidence level.
![Fractalfract 10 00218 g0a1]()
**Figure A1.** Hyperparameter graph of GBR in univariate system.
**Figure A1.** Hyperparameter graph of GBR in univariate system.
![Fractalfract 10 00218 g0a1]()
![Fractalfract 10 00218 g0a2]()
**Figure A2.** Hyperparameter graph of RF in univariate system.
**Figure A2.** Hyperparameter graph of RF in univariate system.
![Fractalfract 10 00218 g0a2]()
![Fractalfract 10 00218 g0a3]()
**Figure A3.** Hyperparameter graph of SVR in univariate system.
**Figure A3.** Hyperparameter graph of SVR in univariate system.
![Fractalfract 10 00218 g0a3]()
![Fractalfract 10 00218 g0a4]()
**Figure A4.** Hyperparameter graph of XGB in univariate system.
**Figure A4.** Hyperparameter graph of XGB in univariate system.
![Fractalfract 10 00218 g0a4]()
![Fractalfract 10 00218 g0a5]()
**Figure A5.** Hyperparameter graph of GBR in multivariate system.
**Figure A5.** Hyperparameter graph of GBR in multivariate system.
![Fractalfract 10 00218 g0a5]()
![Fractalfract 10 00218 g0a6]()
**Figure A6.** Hyperparameter graph of RF in multivariate system.
**Figure A6.** Hyperparameter graph of RF in multivariate system.
![Fractalfract 10 00218 g0a6]()
![Fractalfract 10 00218 g0a7]()
**Figure A7.** Hyperparameter graph of SVR in multivariate system.
**Figure A7.** Hyperparameter graph of SVR in multivariate system.
![Fractalfract 10 00218 g0a7]()
![Fractalfract 10 00218 g0a8]()
**Figure A8.** Hyperparameter graph of XGB in multivariate system.
**Figure A8.** Hyperparameter graph of XGB in multivariate system.
![Fractalfract 10 00218 g0a8]()
![Fractalfract 10 00218 g0a9]()
**Figure A9.** Hyperparameter diagram of the high-frequency component of GBR in the “Sliding EMD” system.
**Figure A9.** Hyperparameter diagram of the high-frequency component of GBR in the “Sliding EMD” system.
![Fractalfract 10 00218 g0a9]()
![Fractalfract 10 00218 g0a10]()
**Figure A10.** Hyperparameter diagram of the high-frequency component of RF in the “Sliding EMD” system.
**Figure A10.** Hyperparameter diagram of the high-frequency component of RF in the “Sliding EMD” system.
![Fractalfract 10 00218 g0a10]()
![Fractalfract 10 00218 g0a11]()
**Figure A11.** Hyperparameter diagram of the high-frequency component of SVR in the “Sliding EMD” system.
**Figure A11.** Hyperparameter diagram of the high-frequency component of SVR in the “Sliding EMD” system.
![Fractalfract 10 00218 g0a11]()
![Fractalfract 10 00218 g0a12]()
**Figure A12.** Hyperparameter diagram of the high-frequency component of XGB in the “Sliding EMD” system.
**Figure A12.** Hyperparameter diagram of the high-frequency component of XGB in the “Sliding EMD” system.
![Fractalfract 10 00218 g0a12]()
![Fractalfract 10 00218 g0a13]()
**Figure A13.** Hyperparameter diagram of the low-frequency component of GBR in the “Sliding EMD” system.
**Figure A13.** Hyperparameter diagram of the low-frequency component of GBR in the “Sliding EMD” system.
![Fractalfract 10 00218 g0a13]()
![Fractalfract 10 00218 g0a14]()
**Figure A14.** Hyperparameter diagram of the low-frequency component of RF in the “Sliding EMD” system.
**Figure A14.** Hyperparameter diagram of the low-frequency component of RF in the “Sliding EMD” system.
![Fractalfract 10 00218 g0a14]()
![Fractalfract 10 00218 g0a15]()
**Figure A15.** Hyperparameter diagram of the low-frequency component of SVR in the “Sliding EMD” system.
**Figure A15.** Hyperparameter diagram of the low-frequency component of SVR in the “Sliding EMD” system.
![Fractalfract 10 00218 g0a15]()
![Fractalfract 10 00218 g0a16]()
**Figure A16.** Hyperparameter diagram of the low-frequency component of XGB in the “Sliding EMD” system.
**Figure A16.** Hyperparameter diagram of the low-frequency component of XGB in the “Sliding EMD” system.
![Fractalfract 10 00218 g0a16]()
![Fractalfract 10 00218 g0a17]()
**Figure A17.** The hyperparameter graph of the GBR high-frequency components of the “Sliding EMD–Multi Variables” system.
**Figure A17.** The hyperparameter graph of the GBR high-frequency components of the “Sliding EMD–Multi Variables” system.
![Fractalfract 10 00218 g0a17]()
![Fractalfract 10 00218 g0a18]()
**Figure A18.** The hyperparameter graph of the RF high-frequency components of the “Sliding EMD–Multi Variables” system.
**Figure A18.** The hyperparameter graph of the RF high-frequency components of the “Sliding EMD–Multi Variables” system.
![Fractalfract 10 00218 g0a18]()
![Fractalfract 10 00218 g0a19]()
**Figure A19.** The hyperparameter graph of the SVR high-frequency components of the “Sliding EMD–Multi Variables” system.
**Figure A19.** The hyperparameter graph of the SVR high-frequency components of the “Sliding EMD–Multi Variables” system.
![Fractalfract 10 00218 g0a19]()
![Fractalfract 10 00218 g0a20]()
**Figure A20.** The hyperparameter graph of the XGB high-frequency components of the “Sliding EMD–Multi Variables” system.
**Figure A20.** The hyperparameter graph of the XGB high-frequency components of the “Sliding EMD–Multi Variables” system.
![Fractalfract 10 00218 g0a20]()
![Fractalfract 10 00218 g0a21]()
**Figure A21.** The hyperparameter graph of the GBR low-frequency components of the “Sliding EMD–Multi Variables” system.
**Figure A21.** The hyperparameter graph of the GBR low-frequency components of the “Sliding EMD–Multi Variables” system.
![Fractalfract 10 00218 g0a21]()
![Fractalfract 10 00218 g0a22]()
**Figure A22.** The hyperparameter graph of the RF low-frequency components of the “Sliding EMD–Multi Variables” system.
**Figure A22.** The hyperparameter graph of the RF low-frequency components of the “Sliding EMD–Multi Variables” system.
![Fractalfract 10 00218 g0a22]()
![Fractalfract 10 00218 g0a23]()
**Figure A23.** The hyperparameter graph of the SVR low-frequency components of the “Sliding EMD–Multi Variables” system.
**Figure A23.** The hyperparameter graph of the SVR low-frequency components of the “Sliding EMD–Multi Variables” system.
![Fractalfract 10 00218 g0a23]()
![Fractalfract 10 00218 g0a24]()
**Figure A24.** The hyperparameter graph of the XGB low-frequency components of the “Sliding EMD–Multi Variables” system.
**Figure A24.** The hyperparameter graph of the XGB low-frequency components of the “Sliding EMD–Multi Variables” system.
![Fractalfract 10 00218 g0a24]()
![Fractalfract 10 00218 g0a25]()
**Figure A25.** Multivariate system prediction result graph.
**Figure A25.** Multivariate system prediction result graph.
![Fractalfract 10 00218 g0a25]()
![Fractalfract 10 00218 g0a26]()
**Figure A26.** The Lasso selection relationship coefficient graph of the multivariable system Nasdaq.
**Figure A26.** The Lasso selection relationship coefficient graph of the multivariable system Nasdaq.
![Fractalfract 10 00218 g0a26]()
![Fractalfract 10 00218 g0a27]()
**Figure A27.** The Lasso selection relationship coefficient graph of the multivariable system Sp500.
**Figure A27.** The Lasso selection relationship coefficient graph of the multivariable system Sp500.
![Fractalfract 10 00218 g0a27]()
![Fractalfract 10 00218 g0a28]()
**Figure A28.** The Lasso choice relationship coefficient diagram of Us monetary policy in a multivariate system.
**Figure A28.** The Lasso choice relationship coefficient diagram of Us monetary policy in a multivariate system.
![Fractalfract 10 00218 g0a28]()
![Fractalfract 10 00218 g0a29]()
**Figure A29.** Comparison of prediction accuracy between the “Sliding EMD-Multi Variables” system and the Multivariate Prediction System.
**Figure A29.** Comparison of prediction accuracy between the “Sliding EMD-Multi Variables” system and the Multivariate Prediction System.
![Fractalfract 10 00218 g0a29]()
![Fractalfract 10 00218 g0a30]()
**Figure A30.** Comparison of prediction accuracy between the “Sliding EMD-Multi Variables” system and the Univariate Prediction System.
**Figure A30.** Comparison of prediction accuracy between the “Sliding EMD-Multi Variables” system and the Univariate Prediction System.
![Fractalfract 10 00218 g0a30]()
![]()
**Table A1.** Error index table of univariate system results.
**Table A1.** Error index table of univariate system results.
| | LR | GBR | RF | SVR | XGB |
|---|---|---|---|---|---|
| MSE\_1 | 3\.54 × 10−4 | 3\.62 × 10−4 | 3\.63 × 10−4 | 3\.65 × 10−4 | 3\.60 × 10−4 |
| RMSE\_1 | 0\.0188 | 0\.0190 | 0\.0190 | 0\.0191 | 0\.0190 |
| MAE\_1 | 0\.0134 | 0\.0135 | 0\.0135 | 0\.0136 | 0\.0134 |
| SMAPE\_1 | 1\.72 | 1\.78 | 1\.74 | 1\.64 | 1\.75 |
| DSTAT\_1 | 0\.510 | 0\.489 | 0\.504 | 0\.503 | 0\.493 |
![]()
**Table A2.** MCS test result table of multivariate system.
**Table A2.** MCS test result table of multivariate system.
| Index | Comparison\_2&1 | |
|---|---|---|
| T R | T S Q | |
| 1 | SVR\_2 (0.000) | SVR\_2 (0.000) |
| 2 | LR\_2 (0.000) | LR\_2 (0.003) |
| 3 | RF\_2 (0.018) | RF\_2 (0.159 \*) |
| 4 | SVR\_1 (0.061) | SVR\_1 (0.269 \*\*) |
| 5 | RF\_1 (0.186 \*) | RF\_1 (0.377 \*\*) |
| 6 | GBR\_1 (0.288 \*\*) | GBR\_1 (0.448 \*\*) |
| 7 | XGB\_1 (0.377 \*\*) | XGB\_1 (0.530 \*\*) |
| 8 | XGB\_2 (0.564 \*\*) | XGB\_2 (0.676 \*\*) |
| 9 | LR\_1 (0.866 \*\*) | LR\_1 (0.866 \*\*) |
| 10 | GBR\_2 (1.000 \*\*) | GBR\_2 (1.000 \*\*) |
**Note:** \*\* and \* denote statistical significance at the 5% and 10% levels, respectively.
![]()
**Table A3.** The result table of Maximum Drawdown Ratio of the “Sliding EMD” system.
**Table A3.** The result table of Maximum Drawdown Ratio of the “Sliding EMD” system.
| Maximum Drawdown Ratio | Comparison\_3&1 | Comparison\_3&2 |
|---|---|---|
| LR | 0\.165 | 0\.629 |
| GBR | 0\.199 | 0\.366 |
| RF | 0\.247 | 0\.519 |
| SVR | 0\.165 | 0\.527 |
| XGB | 0\.198 | 0\.300 |
![]()
**Table A4.** The result table of Sharpe Ratio of the “Sliding EMD” system.
**Table A4.** The result table of Sharpe Ratio of the “Sliding EMD” system.
| Sharpe Ratio | Comparison\_3&1 | Comparison\_3&2 |
|---|---|---|
| LR | 0\.0371 | 3\.77 |
| GBR | 0\.297 | 0\.314 |
| RF | 0\.687 | 1\.42 |
| SVR | 0\.239 | 2\.54 |
| XGB | 0\.533 | 0\.413 |
![]()
**Table A5.** The Sortino Ratio result table of the “Sliding EMD” system.
**Table A5.** The Sortino Ratio result table of the “Sliding EMD” system.
| Sortino Ratio | Comparison\_3&1 | Comparison\_3&2 |
|---|---|---|
| LR | 0\.0905 | 8\.69 |
| GBR | 0\.764 | 0\.857 |
| RF | 1\.79 | 3\.91 |
| SVR | 0\.665 | 6\.71 |
| XGB | 1\.44 | 1\.17 |
![]()
**Table A6.** The Calmar Ratio result table of the “Sliding EMD” system.
**Table A6.** The Calmar Ratio result table of the “Sliding EMD” system.
| Calmar Ratio | Comparison\_3&1 | Comparison\_3&2 |
|---|---|---|
| LR | 0\.0579 | 0\.551 |
| GBR | 0\.128 | 0\.0573 |
| RF | 0\.228 | 0\.330 |
| SVR | 0\.109 | 0\.475 |
| XGB | 0\.230 | 0\.138 |
![]()
**Table A7.** The result table of the Maximum Drawdown Ratio of the “Sliding EMD-Multi Variables” system.
**Table A7.** The result table of the Maximum Drawdown Ratio of the “Sliding EMD-Multi Variables” system.
| Maximum Drawdown Ratio | Comparison\_4&1 | Comparison\_4&2 | Comparison\_4&3 |
|---|---|---|---|
| LR | −0.0173 | 0\.447 | −0.182 |
| GBR | 0\.0961 | 0\.264 | −0.102 |
| RF | 0\.277 | 0\.549 | 0\.0299 |
| SVR | 0\.293 | 0\.655 | 0\.128 |
| XGB | 0\.180 | 0\.281 | −0.0181 |
![]()
**Table A8.** The result table of Sharpe Ratio of the “Sliding EMD-Multi Variables” system.
**Table A8.** The result table of Sharpe Ratio of the “Sliding EMD-Multi Variables” system.
| Sharpe Ratio | Comparison\_4&1 | Comparison\_4&2 | Comparison\_4&3 |
|---|---|---|---|
| LR | −0.385 | 3\.34 | −0.422 |
| GBR | −0.0500 | 0\.0671 | −0.247 |
| RF | 0\.760 | 1\.50 | 0\.0732 |
| SVR | 0\.470 | 2\.78 | 0\.231 |
| XGB | −0.224 | 0\.0562 | −0.357 |
![]()
**Table A9.** The Sortino Ratio result table of the “Sliding EMD-Multi Variables” system.
**Table A9.** The Sortino Ratio result table of the “Sliding EMD-Multi Variables” system.
| Sortino Ratio | Comparison\_4&1 | Comparison\_4&2 | Comparison\_4&3 |
|---|---|---|---|
| LR | −1.12 | 7\.48 | −1.21 |
| GBR | 0\.0465 | 0\.139 | −0.718 |
| RF | 2\.04 | 4\.15 | 0\.250 |
| SVR | 1\.39 | 7\.44 | 0\.726 |
| XGB | 0\.445 | 0\.171 | −0.992 |
![]()
**Table A10.** The Calmar Ratio result table of the “Sliding EMD-Multi Variables” system.
**Table A10.** The Calmar Ratio result table of the “Sliding EMD-Multi Variables” system.
| Calmar Ratio | Comparison\_4&1 | Comparison\_4&2 | Comparison\_4&3 |
|---|---|---|---|
| LR | −0.144 | 0\.349 | −0.202 |
| GBR | 0\.0412 | −0.0296 | −0.0868 |
| RF | 0\.252 | 0\.354 | 0\.0242 |
| SVR | 0\.202 | 0\.568 | 0\.0924 |
| XGB | 0\.0498 | −0.0423 | −0.180 |
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![Fractalfract 10 00218 g005]()
**Figure 5.** Figure of the ADA daily closing price and return series.
**Figure 5.** Figure of the ADA daily closing price and return series.
![Fractalfract 10 00218 g005]()
![Fractalfract 10 00218 g006]()
**Figure 6.** The time series graph of the four main variables. Note: [Figure 5](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-f005) and [Figure 6](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-f006) are plotted by the authors based on raw data collected from multiple sources.
**Figure 6.** The time series graph of the four main variables. Note: [Figure 5](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-f005) and [Figure 6](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-f006) are plotted by the authors based on raw data collected from multiple sources.
![Fractalfract 10 00218 g006]()
![Fractalfract 10 00218 g007]()
**Figure 7.** LASSO dynamic factor selection results for high-frequency components. Note: [Figure 7](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-f007), [Figure 8](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-f008), [Figure 9](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-f009) and [Figure 10](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-f010) illustrate the LASSO-based dynamic factor selection results and their time-varying coefficients, and were produced by the authors.
**Figure 7.** LASSO dynamic factor selection results for high-frequency components. Note: [Figure 7](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-f007), [Figure 8](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-f008), [Figure 9](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-f009) and [Figure 10](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-f010) illustrate the LASSO-based dynamic factor selection results and their time-varying coefficients, and were produced by the authors.
![Fractalfract 10 00218 g007]()
![Fractalfract 10 00218 g008]()
**Figure 8.** Dynamic coefficient plot of high-frequency factors in the “Sliding EMD–Multi Variables” prediction system.
**Figure 8.** Dynamic coefficient plot of high-frequency factors in the “Sliding EMD–Multi Variables” prediction system.
![Fractalfract 10 00218 g008]()
![Fractalfract 10 00218 g009]()
**Figure 9.** LASSO dynamic factor plot for low-frequency components.
**Figure 9.** LASSO dynamic factor plot for low-frequency components.
![Fractalfract 10 00218 g009]()
![Fractalfract 10 00218 g010]()
**Figure 10.** Dynamic coefficient plot of low-frequency factors in the “Sliding EMD–Multi Variables” prediction system.
**Figure 10.** Dynamic coefficient plot of low-frequency factors in the “Sliding EMD–Multi Variables” prediction system.
![Fractalfract 10 00218 g010]()
![Fractalfract 10 00218 g011]()
**Figure 11.** Comparison of prediction accuracy between the “Sliding EMD” system and the Univariate Prediction System. Note: The radar chart shows percentage data. The closer to the center of the origin, the smaller the data becomes. The further out the data, the greater the percentage, and the stronger the improvement percentage in the comparison between the two systems.
**Figure 11.** Comparison of prediction accuracy between the “Sliding EMD” system and the Univariate Prediction System. Note: The radar chart shows percentage data. The closer to the center of the origin, the smaller the data becomes. The further out the data, the greater the percentage, and the stronger the improvement percentage in the comparison between the two systems.
![Fractalfract 10 00218 g011]()
![]()
**Table 1.** Error metrics for the Multivariate Prediction System.
**Table 1.** Error metrics for the Multivariate Prediction System.
| | LR | GBR | RF | SVR | XGB |
|---|---|---|---|---|---|
| MSE\_2 | 4\.05 × 10−4 | 3\.52 × 10−4 | 3\.71 × 10−4 | 4\.13 × 10−4 | 3\.59 × 10−4 |
| RMSE\_2 | 0\.0201 | 0\.0188 | 0\.0193 | 0\.0203 | 0\.0189 |
| MAE\_2 | 0\.0145 | 0\.0133 | 0\.0136 | 0\.0146 | 0\.0134 |
| SMAPE\_2 | 1\.73 | 1\.74 | 1\.73 | 1\.73 | 1\.74 |
| DSTAT\_2 | 0\.381 | 0\.487 | 0\.447 | 0\.367 | 0\.482 |
![]()
**Table 2.** Comparison of the Multivariate Prediction System with the Univariate Prediction System.
**Table 2.** Comparison of the Multivariate Prediction System with the Univariate Prediction System.
| Comparison\_2&1 | LR | GBR | RF | SVR | XGB |
|---|---|---|---|---|---|
| MSE\_21 | −14.46% | 2\.64% | −2.17% | −13.41% | 0\.29% |
| RMSE\_21 | −6.98% | 1\.33% | −1.08% | −6.49% | 0\.15% |
| MAE\_21 | −8.25% | 1\.57% | −0.83% | −7.53% | 0\.18% |
| SMAPE\_21 | −1.03% | 2\.07% | 0\.60% | −5.23% | 0\.73% |
| DSTAT\_21 | −25.26% | −0.26% | −11.35% | −26.97% | −2.29% |
Note: A “−” indicates worse forecast performance.
![]()
**Table 3.** Error metrics for the “Sliding EMD” system.
**Table 3.** Error metrics for the “Sliding EMD” system.
| | LR | GBR | RF | SVR | XGB |
|---|---|---|---|---|---|
| MSE\_3 | 3\.53 × 10−4 | 3\.57 × 10−4 | 3\.58 × 10−4 | 3\.62 × 10−4 | 3\.57 × 10−4 |
| RMSE\_3 | 0\.0188 | 0\.0189 | 0\.0189 | 0\.0190 | 0\.0189 |
| MAE\_3 | 0\.0134 | 0\.0135 | 0\.0135 | 0\.0136 | 0\.0135 |
| SMAPE\_3 | 1\.64 | 1\.66 | 1\.64 | 1\.59 | 1\.65 |
| DSTAT\_3 | 0\.510 | 0\.500 | 0\.494 | 0\.504 | 0\.500 |
![]()
**Table 4.** MCS test results for the “Sliding EMD” system.
**Table 4.** MCS test results for the “Sliding EMD” system.
| Index | Comparison\_3&1 | Comparison\_3&2 | | |
|---|---|---|---|---|
| | T R | T S Q | T R | T S Q |
| 1 | SVR\_1 (0.168 \*) | SVR\_1 (0.182 \*) | SVR\_2 (0.000) | SVR\_2 (0.000) |
| 2 | RF\_1 (0.255 \*\*) | RF\_1 (0.270 \*\*) | LR\_2 (0.000) | LR\_2 (0.000) |
| 3 | SVR\_3 (0.255 \*\*) | SVR\_3 (0.305 \*\*) | RF\_2 (0.016) | RF\_2 (0.208 \*\*) |
| 4 | GBR\_1 (0.438 \*\*) | GBR\_1 (0.424 \*\*) | SVR\_3 (0.134 \*) | SVR\_3 (0.396 \*\*) |
| 5 | XGB\_1 (0.629 \*\*) | XGB\_1 (0.538 \*\*) | RF\_3 (0.633 \*\*) | RF\_3 (0.657 \*\*) |
| 6 | RF\_3 (0.659 \*\*) | RF\_3 (0.546 \*\*) | GBR\_3 (0.633 \*\*) | GBR\_3 (0.657 \*\*) |
| 7 | GBR\_3 (0.659 \*\*) | GBR\_3 (0.550 \*\*) | XGB\_2 (0.633 \*\*) | XGB\_2 (0.657 \*\*) |
| 8 | XGB\_3 (0.659 \*\*) | XGB\_3 (0.550 \*\*) | XGB\_3 (0.633 \*\*) | XGB\_3 (0.657 \*\*) |
| 9 | LR\_1 (0.868 \*\*) | LR\_1 (0.868 \*\*) | LR\_3 (0.934 \*\*) | LR\_3 (0.934 \*\*) |
| 10 | LR\_3 (1.000 \*\*) | LR\_3 (1.000 \*\*) | GBR\_2 (1.000 \*\*) | GBR\_2 (1.000 \*\*) |
**Note:** In [Table 4](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-t004) and in subsequent tables presenting Model Confidence Set test results, asterisks indicate the following significance levels: \* denotes significance at α = 0.05, and \*\* denotes significance at α = 0.01.
![]()
**Table 5.** Daily return comparison for the “Sliding EMD” system.
**Table 5.** Daily return comparison for the “Sliding EMD” system.
| Daily Return | Comparison\_3&1 | Comparison\_3&2 |
|---|---|---|
| LR | 9\.00 × 10−5 | 2\.64 × 10−3 |
| GBR | 3\.63 × 10−4 | 3\.76 × 10−4 |
| RF | 5\.74 × 10−4 | 1\.35 × 10−3 |
| SVR | 2\.50 × 10−4 | 2\.27 × 10−3 |
| XGB | 5\.43 × 10−4 | 4\.24 × 10−4 |
![]()
**Table 6.** Error metrics for the “Sliding EMD–Multi Variables” system.
**Table 6.** Error metrics for the “Sliding EMD–Multi Variables” system.
| | LR | GBR | RF | SVR | XGB |
|---|---|---|---|---|---|
| MSE\_4 | 3\.50 × 10−4 | 3\.57 × 10−4 | 3\.56 × 10−4 | 3\.56 × 10−4 | 3\.56 × 10−4 |
| RMSE\_4 | 0\.0187 | 0\.0189 | 0\.0189 | 0\.0189 | 0\.0189 |
| MAE\_4 | 0\.0133 | 0\.0135 | 0\.0135 | 0\.0135 | 0\.0135 |
| SMAPE\_4 | 1\.68 | 1\.68 | 1\.68 | 1\.67 | 1\.69 |
| DSTAT\_4 | 0\.507 | 0\.485 | 0\.504 | 0\.514 | 0\.493 |
![]()
**Table 7.** MCS test results for the “Sliding EMD–Multi Variables” system.
**Table 7.** MCS test results for the “Sliding EMD–Multi Variables” system.
| Index | Comparison\_4&1 | Comparison\_4&2 | Comparison\_4&3 | | | |
|---|---|---|---|---|---|---|
| | T R | T S Q | T R | T S Q | T R | T S Q |
| 1 | SVR\_1 (0.105 \*) | SVR\_1 (0.108 \*) | SVR\_2 (0.000) | SVR\_2 (0.000) | SVR\_3 (0.275 \*\*) | SVR\_3 (0.222 \*\*) |
| 2 | RF\_1 (0.312 \*\*) | RF\_1 (0.187 \*) | LR\_2 (0.000) | LR\_2 (0.000) | GBR\_4 (0.309 \*\*) | GBR\_4 (0.327 \*\*) |
| 3 | GBR\_1 (0.312 \*\*) | GBR\_1 (0.253 \*\*) | RF\_2 (0.016) | RF\_2 (0.224 \*\*) | RF\_3 (0.309 \*\*) | RF\_3 (0.327 \*\*) |
| 4 | GBR\_4 (0.312 \*\*) | GBR\_4 (0.283 \*\*) | GBR\_4 (0.188 \*) | GBR\_4 (0.456 \*\*) | XGB\_4 (0.309 \*\*) | XGB\_4 (0.327 \*\*) |
| 5 | XGB\_1 (0.312 \*\*) | XGB\_1 (0.283 \*\*) | XGB\_4 (0.188 \*) | XGB\_4 (0.462 \*\*) | RF\_4 (0.494 \*\*) | RF\_4 (0.327 \*\*) |
| 6 | XGB\_4 (0.312 \*\*) | XGB\_4 (0.283 \*\*) | SVR\_4 (0.351 \*\*) | SVR\_4 (0.518 \*\*) | GBR\_3 (0.494 \*\*) | GBR\_3 (0.327 \*\*) |
| 7 | SVR\_4 (0.312 \*\*) | SVR\_4 (0.283 \*\*) | XGB\_2 (0.351 \*\*) | XGB\_2 (0.518 \*\*) | SVR\_4 (0.494 \*\*) | SVR\_4 (0.327 \*\*) |
| 8 | RF\_4 (0.312 \*\*) | RF\_4 (0.283 \*\*) | RF\_4 (0.351 \*\*) | RF\_4 (0.518 \*\*) | XGB\_3 (0.494 \*\*) | XGB\_3 (0.327 \*\*) |
| 9 | LR\_1 (0.488 \*\*) | LR\_1 (0.488 \*\*) | GBR\_2 (0.997 \*\*) | GBR\_2 (0.997 \*\*) | LR\_3 (0.520 \*\*) | LR\_3 (0.520 \*\*) |
| 10 | LR\_4 (1.000 \*\*) | LR\_4 (1.000 \*\*) | LR\_4 (1.000 \*\*) | LR\_4 (1.000 \*\*) | LR\_4 (1.000 \*\*) | LR\_4 (1.000 \*\*) |
**Note:** In [Table 7](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-t007), asterisks indicate the following significance levels: \* denotes significance at α = 0.05, and \*\* denotes significance at α = 0.01.
![]()
**Table 8.** Comparison with the most relevant studies.
**Table 8.** Comparison with the most relevant studies.
| | Study (Year) | Method | Sliding Window? | Other Predictive Variables? | Potential Future Data Leakage? | Key Empirical Findings/Investment Implications |
|---|---|---|---|---|---|---|
| **1** | Xu and Niu (2023) \[[13](https://www.mdpi.com/2504-3110/10/4/218#B13-fractalfract-10-00218)\] | EMD/VMD-KNN | Yes | Yes (not enough) | No, sliding ensures real-time updates | Decomposition–reconstruction method helps filter out noise from crude oil price time series, improving the prediction accuracy. |
| **2** | Kim et al. (2021) \[[25](https://www.mdpi.com/2504-3110/10/4/218#B25-fractalfract-10-00218)\] | SVR, RF, XGB | No | Yes (only one type of variable) | Yes, full-sample data used | Combining Blockchain data with machine learning algorithms significantly improves the accuracy of Ethereum price forecasts. Investors can analyze Blockchain data, leading to better entry/exit points in the market. |
| **3** | Fallah et al. (2024) \[[26](https://www.mdpi.com/2504-3110/10/4/218#B26-fractalfract-10-00218)\] | LSTM-GRU | Yes | Yes (not enough) | No, sliding ensures real-time updates | Integrating error correction mechanisms into deep learning models improves the prediction accuracy for cryptocurrency prices. This model can provide more accurate price predictions, reducing risk and enhancing decision-making. |
| **4** | Wang et al. (2023) \[[23](https://www.mdpi.com/2504-3110/10/4/218#B23-fractalfract-10-00218)\] | SVM, GBR | Yes | Yes (only three types of variables) | No, sliding ensures real-time updates | Machine learning models, when combined with both internal and external determinants, can significantly improve the prediction of cryptocurrency volatility. Investors can use these insights to better improve risk management and trading strategies. |
| **5** | Qiu et al. (2025) \[[24](https://www.mdpi.com/2504-3110/10/4/218#B24-fractalfract-10-00218)\] | ARIMA-GARCH-LSTM | Yes | Yes (only three types of variables) | No, sliding ensures real-time updates | The model clustering approach enhances volatility forecasting by combining the strengths of multiple models. Investors can use this approach to gain a more reliable forecast of cryptocurrency volatility. |
| **6** | Zhang et al. (2023) \[[12](https://www.mdpi.com/2504-3110/10/4/218#B12-fractalfract-10-00218)\] | VMD-GRU | Yes | Yes (not enough) | No, sliding ensures real-time updates | The model provides improved accuracy in forecasting oil prices by effectively capturing both short-term and long-term trends in the price movements. This approach offers oil traders and investors a powerful tool for predicting price movements, improving trading strategies and hedging decisions. |
| **7** | Li et al. (2022) \[[28](https://www.mdpi.com/2504-3110/10/4/218#B28-fractalfract-10-00218)\] | LR | No | Yes (enough) | Yes, full-sample data used | The study finds that art pricing can be effectively modeled by considering both historical returns and risk factors. Investors in the art market can use these insights to assess the risk and return potential of artworks at auction. |
| **8** | Hajek et al. (2023) \[[42](https://www.mdpi.com/2504-3110/10/4/218#B42-fractalfract-10-00218)\] | RF-XGB-Gradient Boosting | Yes | Yes (enough) | No, sliding ensures real-time updates | The study demonstrates that investor sentiment can significantly improve the prediction of Bitcoin prices. Investors can predict price trends more accurately by considering both market data and sentiment, leading to better timing for Bitcoin investments. |
| | |
|---|---|
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© 2026 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the [Creative Commons Attribution (CC BY) license](https://creativecommons.org/licenses/by/4.0/).
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Zhang, W.; Tang, Z.; Zhuang, X.; Cai, Y.; Dong, B. Cryptocurrency Price Prediction Using Sliding Empirical Mode Decomposition with Economic Variables: A Machine Learning Approach. *Fractal Fract.* **2026**, *10*, 218. https://doi.org/10.3390/fractalfract10040218
**AMA Style**
Zhang W, Tang Z, Zhuang X, Cai Y, Dong B. Cryptocurrency Price Prediction Using Sliding Empirical Mode Decomposition with Economic Variables: A Machine Learning Approach. *Fractal and Fractional*. 2026; 10(4):218. https://doi.org/10.3390/fractalfract10040218
**Chicago/Turabian Style**
Zhang, Wenhao, Zhenpeng Tang, Xiaowen Zhuang, Yi Cai, and Baihua Dong. 2026. "Cryptocurrency Price Prediction Using Sliding Empirical Mode Decomposition with Economic Variables: A Machine Learning Approach" *Fractal and Fractional* 10, no. 4: 218. https://doi.org/10.3390/fractalfract10040218
**APA Style**
Zhang, W., Tang, Z., Zhuang, X., Cai, Y., & Dong, B. (2026). Cryptocurrency Price Prediction Using Sliding Empirical Mode Decomposition with Economic Variables: A Machine Learning Approach. *Fractal and Fractional*, *10*(4), 218. https://doi.org/10.3390/fractalfract10040218
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Zhang, W.; Tang, Z.; Zhuang, X.; Cai, Y.; Dong, B. Cryptocurrency Price Prediction Using Sliding Empirical Mode Decomposition with Economic Variables: A Machine Learning Approach. *Fractal Fract.* **2026**, *10*, 218. https://doi.org/10.3390/fractalfract10040218
**AMA Style**
Zhang W, Tang Z, Zhuang X, Cai Y, Dong B. Cryptocurrency Price Prediction Using Sliding Empirical Mode Decomposition with Economic Variables: A Machine Learning Approach. *Fractal and Fractional*. 2026; 10(4):218. https://doi.org/10.3390/fractalfract10040218
**Chicago/Turabian Style**
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**APA Style**
Zhang, W., Tang, Z., Zhuang, X., Cai, Y., & Dong, B. (2026). Cryptocurrency Price Prediction Using Sliding Empirical Mode Decomposition with Economic Variables: A Machine Learning Approach. *Fractal and Fractional*, *10*(4), 218. https://doi.org/10.3390/fractalfract10040218
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| Readable Markdown | ## 1\. Introduction
Cardano cryptocurrency (ADA) holds a significant position in the cryptocurrency market, ranking among the top ten globally with a market capitalization of around 26.17 billion USD. Its growing institutional recognition is underscored by major financial infrastructure developments, such as CME Group’s announced plan to launch ADA-linked futures contracts, reflecting its established liquidity and maturation within the digital asset ecosystem (<https://www.nasdaq.com/press-release/cme-group-expand-crypto-derivatives-suite-launch-cardano-chainlink-and-stellar>, accessed on 15 January 2026). Cardano utilizes the Ouroboros proof-of-stake consensus mechanism, which its founder estimates consumes less than 0.01% of the energy compared to the Bitcoin network (<https://www.the-independent.com/space/cardano-crypto-bitcoin-elon-musk-b1849021.html>, accessed on 18 May 2021). This energy efficiency has drawn the attention of investors focused on ESG (Environmental, Social, and Governance) criteria \[[1](https://www.mdpi.com/2504-3110/10/4/218#B1-fractalfract-10-00218)\].
ADA’s price volatility is highly susceptible to shifts in macroeconomic conditions and broader financial environments. Elsayed et al. (2022) \[[2](https://www.mdpi.com/2504-3110/10/4/218#B2-fractalfract-10-00218)\] found a synergistic effect between the macroeconomic environment and cryptocurrency trading volumes. Feng et al. (2025) \[[3](https://www.mdpi.com/2504-3110/10/4/218#B3-fractalfract-10-00218)\] argued that changes in regulatory policies have increased the volatility of cryptocurrency prices. Aharon et al. (2021) \[[4](https://www.mdpi.com/2504-3110/10/4/218#B4-fractalfract-10-00218)\] discovered a dynamic correlation between the US dollar exchange rate and cryptocurrency prices. There is also risk contagion between different cryptocurrencies \[[5](https://www.mdpi.com/2504-3110/10/4/218#B5-fractalfract-10-00218)\]. Moreover, the connections between traditional financial markets and cryptocurrencies have become more frequent \[[6](https://www.mdpi.com/2504-3110/10/4/218#B6-fractalfract-10-00218)\]. Consequently, incorporating such external determinants into forecasting models is crucial for improving prediction performance and understanding the multi-scale drivers of ADA prices.
The volatility of ADA prices and its impact on the economy and financial markets have attracted significant academic attention. ADA’s market value fluctuations affect the consumption sector through wealth effects and, via chain reactions, influence upstream and downstream companies in the blockchain industry \[[7](https://www.mdpi.com/2504-3110/10/4/218#B7-fractalfract-10-00218)\]. This price instability increases the systemic risk premium in the cryptocurrency market, transferring risk to the traditional financial system through cross-market correlations. Notably, ADA’s price exhibits volatility clustering, long-range dependence, and multifractal characteristics across different time scales, reflecting the complex nonlinear dynamics inherent in cryptocurrency markets \[[8](https://www.mdpi.com/2504-3110/10/4/218#B8-fractalfract-10-00218)\]. These multi-scale fractal properties challenge classical financial time series models that assume linear relationships and stationary processes. As a result, developing a stable and reliable prediction system that accounts for multi-scale dynamics is crucial for ADA.
Current cryptocurrency price prediction methods have evolved from traditional econometric models to machine learning techniques and “decomposition–ensemble” hybrid methods \[[9](https://www.mdpi.com/2504-3110/10/4/218#B9-fractalfract-10-00218)\]. Econometric models face limitations in capturing non-linear features \[[10](https://www.mdpi.com/2504-3110/10/4/218#B10-fractalfract-10-00218)\], while machine learning methods can excel in modeling complex patterns \[[11](https://www.mdpi.com/2504-3110/10/4/218#B11-fractalfract-10-00218)\]. However, when dealing with multi-scale, nonlinear signal data like cryptocurrency returns, even single machine learning algorithms may not achieve ideal predictive performance without using hybrid models like “decomposition–ensemble” \[[12](https://www.mdpi.com/2504-3110/10/4/218#B12-fractalfract-10-00218)\].
The “decomposition and ensemble” framework, rooted in multi-scale signal processing and fractal analysis, can decompose complex financial signals into multiple frequency components corresponding to different time scales. This multi-resolution approach aligns with the hierarchical structure of financial market dynamics, where short-term trading behavior and long-term macroeconomic trends operate at distinct temporal scales. Next, it applies ensemble-based recombination techniques to filter out extraneous noise. By forecasting each meaningful component separately and then summing those forecasts, this “divide-and-conquer” approach improves the accuracy of detecting complex multi-scale dynamics. However, decomposition methods applied to the full sample may result in information leakage, as the decomposition of historical data points can be influenced by the statistical properties of future data when the entire series is processed at once, thereby contaminating the training set with information that would not be available in a realistic sliding forecasting setting. Several scholars have explored algorithms like sliding VMD and sliding EEMD for financial asset price prediction \[[13](https://www.mdpi.com/2504-3110/10/4/218#B13-fractalfract-10-00218)\]. However, research on applying sliding decomposition algorithms that preserve the temporal hierarchy to cryptocurrency return prediction is still limited. To address the information leakage issue inherent in full-sample decomposition, the sliding window approach processes data sequentially, ensuring that each training set uses only information available up to that point. This preserves the temporal hierarchy and prevents future information from contaminating the prediction process, making it a methodologically sound framework for cryptocurrency return forecasting. Additionally, incorporating essential factors, such as key policy and economic variables, at different frequency scales into sliding decomposition algorithms will enhance the understanding of the multi-scale drivers of ADA prices and assist cryptocurrency market investors in optimizing their portfolios.
To address the limitations mentioned above, this study focuses on the following questions: Does sliding decomposition that captures multi-scale dynamics improve the accuracy of ADA return predictions compared to traditional non-decomposed frameworks? Based on the existing literature, can incorporating key economic variables at the component level across different time scales into the prediction model enhance the forecasting performance for ADA? Which method, variable-driven or multi-scale sliding decomposition, leads to greater improvements in prediction? Can investment performance based on fractal-based sliding decomposition provide better results, helping investors make more informed decisions?
This research evaluates and compares four different forecasting frameworks: a Univariate Prediction System (System 1), a Multivariate Prediction System (System 2), the “Sliding EMD” prediction system (System 3), and the “Sliding EMD–Multi Variables” prediction system (System 4). Comparing System 2 with System 1 allows for testing whether incorporating influencing factors into the raw ADA series improves prediction accuracy. The comparison between System 3 and System 1 examines whether the Sliding EMD that captures multi-scale fractal properties can improve forecasting accuracy compared to a non-decomposed univariate system. The comparison between System 3 and System 2 demonstrates the relative advantages of multivariate and multi-scale decomposition approaches. Lastly, the comparison between System 4 and System 3 tests whether incorporating factors at the component level across different frequency scales in the “Sliding EMD” framework can further enhance prediction.
The innovation of this study lies in the following aspects: First, this study directly compares the “Sliding EMD” framework that exploits multi-scale temporal structures with traditional frameworks to evaluate the effectiveness of sliding decomposition technology in ADA prediction. To avoid the data leakage issue caused by applying traditional full-sample decomposition algorithms to ADA returns, this study uses the Sliding EMD method with a fixed window to predict ADA returns. Unlike existing studies that apply sliding decomposition, we employ unsupervised K-means clustering to adaptively group the derived components into high- and low-frequency clusters based on their intrinsic statistical properties. This clustering approach leverages the natural frequency separation inherent in EMD’s multi-scale decomposition, allowing us to capture both rapid market fluctuations and gradual trend movements. This approach not only integrates information from different frequency components to enhance prediction performance but also lays the foundation for further incorporating the impact of economic variables on different frequency scales.
Second, leveraging existing research on ADA’s influential factors, seven main categories of influencing variables are identified: macroeconomic variables, social variables, exchange rate variables, competitive variables, financial variables, commodity variables, and policy variables. Using Least Absolute Shrinkage and Selection Operator (LASSO) regression, significant variables influencing both the raw returns and decomposed components at different time scales are determined. The dynamic factor selection process using LASSO can be integrated into the Univariate Prediction System to form a Multivariate Prediction System. When incorporated into the “Sliding EMD” system, this results in the “Sliding EMD–Multi Variables” system that accounts for scale-dependent economic influences.
Finally, based on rigorous error metrics and statistical tests, this study yields three key insights that advance our understanding of ADA return forecasting. First, the multi-scale Sliding EMD framework exerts a stronger influence on prediction accuracy than dynamic factor selection via LASSO. Second, the prediction performance of the Sliding EMD system consistently surpasses that of the multivariate system. Third, the “Sliding EMD–Multi Variables” system delivers a slight improvement over the “Sliding EMD” system, further enhancing forecasting accuracy. This system integrates fractal-based decomposition with scale-specific economic variables, while the conventional multivariate approach proves comparatively ineffective. These findings collectively affirm that the predictability of ADA returns is fundamentally shaped by economic factors operating across distinct frequency components and time scales. To demonstrate the practical utility of these insights, we conduct an investment performance analysis, which confirms that the proposed framework aids investors in optimizing portfolio allocation, enhancing risk-adjusted returns, and mitigating downside risk, thereby offering actionable guidance for financial decision-making.
The structure of this paper is as follows: [Section 2](https://www.mdpi.com/2504-3110/10/4/218#sec2-fractalfract-10-00218) provides a literature review on the main drivers and prediction methods for ADA; [Section 3](https://www.mdpi.com/2504-3110/10/4/218#sec3-fractalfract-10-00218) details the four prediction frameworks employed in this study for ADA returns; [Section 4](https://www.mdpi.com/2504-3110/10/4/218#sec4-fractalfract-10-00218) analyzes ADA returns and key variables used in this study, with a discussion on the variables selected via LASSO; [Section 5](https://www.mdpi.com/2504-3110/10/4/218#sec5-fractalfract-10-00218) presents a comparison of the prediction results of the four frameworks for ADA returns, performance tests, and corresponding investment performance comparisons; [Section 6](https://www.mdpi.com/2504-3110/10/4/218#sec6-fractalfract-10-00218) discusses the research findings; and [Section 7](https://www.mdpi.com/2504-3110/10/4/218#sec7-fractalfract-10-00218) concludes the study with investment insights.
## 2\. Literature Review
### 2\.1. Key Drivers of ADA Price
As a prominent cryptocurrency, ADA exhibits significant return correlations with other major digital assets. This interdependence stems from shared market mechanisms and investor psychology. Specifically, price appreciation in large-capitalization cryptocurrencies such as Bitcoin and Ethereum, which is typically driven by institutional inflows, favorable regulatory developments, or broader macroeconomic tailwinds, tends to increase overall market risk appetite. This shift in sentiment encourages capital to flow across the cryptocurrency ecosystem, activating price transmission channels that subsequently elevate ADA’s valuation \[[7](https://www.mdpi.com/2504-3110/10/4/218#B7-fractalfract-10-00218)\]. Moreover, ADA is primarily traded against Bitcoin (ADA/BTC) and stablecoins such as USDT (ADA/USDT). Consequently, pronounced fluctuations in Bitcoin often induce passive, correlation-driven adjustments in the ADA/BTC pair, while ADA/USDT valuations remain additionally exposed to shifts in overall market sentiment and liquidity conditions \[[14](https://www.mdpi.com/2504-3110/10/4/218#B14-fractalfract-10-00218)\].
ADA’s price dynamics are significantly shaped by macroeconomic and policy variables, including exchange rates, economic uncertainty indices, and fiscal and monetary policies. Exchange-rate movements, particularly in the U.S. dollar, exert a notable pressure on cryptocurrency valuations: a strengthening dollar typically dampens investor appetite for risk assets, leading to downward pressure on ADA’s price \[[4](https://www.mdpi.com/2504-3110/10/4/218#B4-fractalfract-10-00218)\]. Concurrently, heightened economic policy uncertainty elevates perceived risk within the cryptocurrency sector, which further suppresses ADA’s market performance \[[2](https://www.mdpi.com/2504-3110/10/4/218#B2-fractalfract-10-00218)\]. Conversely, ADA may serve as an effective inflation-hedging instrument; rising inflation expectations often drive capital toward cryptocurrencies as stores of value, thereby boosting ADA’s price \[[15](https://www.mdpi.com/2504-3110/10/4/218#B15-fractalfract-10-00218)\]. Moreover, accommodative fiscal and monetary policies stimulate liquidity and risk-taking sentiment, indirectly fostering bullish conditions in the cryptocurrency market and supporting ADA’s upward momentum \[[16](https://www.mdpi.com/2504-3110/10/4/218#B16-fractalfract-10-00218)\].
The price of ADA is notably influenced by developments in both financial and commodity markets. In equity markets, fluctuations in stock prices can generate spillover effects on cryptocurrency valuations. As demonstrated by Attarzadeh et al. (2024) \[[17](https://www.mdpi.com/2504-3110/10/4/218#B17-fractalfract-10-00218)\], a measurable transmission of volatility and returns from traditional equities to ADA exists, a linkage that typically reflects concurrent shifts in broader risk sentiment and liquidity conditions affecting both asset classes. Meanwhile, commodity markets exert influence through a more structural channel, since the operational costs of blockchain networks depend substantially on hardware components, including specialized metals used in mining hardware and energy consumption, whose prices are tied directly to commodity cycles. Rising costs in these inputs, as noted by Jiang et al. (2025) \[[18](https://www.mdpi.com/2504-3110/10/4/218#B18-fractalfract-10-00218)\], can constrain network expansion and operational efficiency, thereby indirectly pressuring the valuation of cryptocurrencies such as ADA.
Online sentiment and extreme events constitute critical external drivers of ADA’s price dynamics. Investor attention, often proxied by search volumes on platforms such as Google, reflects real-time shifts in retail and speculative interest. As noted by Aslanidis et al. (2024) \[[19](https://www.mdpi.com/2504-3110/10/4/218#B19-fractalfract-10-00218)\] and Hoang et al. (2024) \[[20](https://www.mdpi.com/2504-3110/10/4/218#B20-fractalfract-10-00218)\], this attention can rapidly translate into trading pressure and price momentum for cryptocurrencies including ADA. Beyond mere attention metrics, broader sentiment extracted from social media and news coverage further amplifies short-term volatility, as herd behavior frequently characterizes cryptocurrency markets. Extreme events, including geopolitical conflicts, trade disputes, or large-scale natural disasters, introduce sudden uncertainty and risk-off sentiment across global markets, triggering pronounced fluctuations in cryptocurrency valuations. Moreover, regulatory and policy announcements, particularly from influential jurisdictions like the United States, directly shape market structure and investor confidence. Będowska et al. (2024) \[[21](https://www.mdpi.com/2504-3110/10/4/218#B21-fractalfract-10-00218)\] highlight that the official stance of U.S. authorities toward digital assets can alter liquidity conditions, institutional participation, and long-term adoption prospects, thereby exerting a sustained influence on ADA’s market trajectory.
Time-scale decomposition is theoretically and empirically essential for cryptocurrency forecasting, as it aligns with the Heterogeneous Market Hypothesis (HMH). The HMH posits that market participants operate on distinct investment horizons, driving price formation at multiple frequencies. Low-frequency components predominantly reflect fundamental macroeconomic forces, which evolve slowly and anchor the intrinsic value of assets. In contrast, high-frequency components capture transient market microstructure noise, including speculative trading, liquidity shocks, and immediate reactions to exogenous events. By isolating these frequency bands, predictive models can disentangle the distinct economic mechanisms at play: macroeconomic fundamentals govern long-term trends, while short-term volatility is driven by information asymmetry and behavioral factors \[[22](https://www.mdpi.com/2504-3110/10/4/218#B22-fractalfract-10-00218)\]. This separation not only enhances forecast accuracy by reducing noise interference but also provides critical insights into cryptocurrency market dynamics, such as the differential impact of financial factors (high-frequency) versus monetary and fiscal policies (low-frequency). Thus, frequency-aware modeling is not merely a technical refinement, but also a theoretically grounded necessity for robust cryptocurrency prediction.
The existing literature has identified numerous economic and financial factors affecting ADA returns, yet seldom integrates them dynamically into predictive models. This limits both explanatory power and forecast accuracy. Our study addresses this gap by implementing a factor-informed prediction architecture that combines sliding window decomposition with LASSO-based dynamic variable selection. This approach captures scale-dependent and time-varying effects of key drivers, enhances interpretability, and provides an actionable framework for improving prediction accuracy and supporting investment decisions.
### 2\.2. Cryptocurrency Price Prediction Methods
Forecasting cryptocurrency asset prices can be clearly divided into three approaches: traditional econometric models, machine learning, and the “decomposition–ensemble” system \[[23](https://www.mdpi.com/2504-3110/10/4/218#B23-fractalfract-10-00218)\]. Traditional econometric models mainly include ARIMA, GARCH family, and HAR family models \[[24](https://www.mdpi.com/2504-3110/10/4/218#B24-fractalfract-10-00218)\]. However, these models have strict assumptions, such as the linearity and stationarity of time series. Although some econometric models have developed new methods applicable to nonlinear data, overall, econometric models still exhibit significant limitations when it comes to capturing the complex financial time series signals of cryptocurrencies.
Machine learning emerged in the context of big data and artificial intelligence, with traditional machine learning algorithms such as Support Vector Machines (SVMs), Random Forest (RF), and Gradient Boosting Decision Trees (GBDTs) being commonly used in financial asset price prediction \[[25](https://www.mdpi.com/2504-3110/10/4/218#B25-fractalfract-10-00218)\]. Long Short-Term Memory (LSTM) networks and Convolutional Neural Networks (CNNs) are classic deep learning algorithms for cryptocurrency prediction \[[26](https://www.mdpi.com/2504-3110/10/4/218#B26-fractalfract-10-00218)\]. Overall, both traditional machine learning and deep learning can effectively capture the nonlinear characteristics of time series. However, in the 24/7 cryptocurrency market, the complex, chaotic features still compel researchers to turn to the development of hybrid models.
While deep learning models such as LSTM and GRU can capture complex nonlinear patterns in cryptocurrency forecasting, they frequently exhibit prediction instability manifested through output oscillations and heightened sensitivity to initialization and hyperparameter configurations \[[27](https://www.mdpi.com/2504-3110/10/4/218#B27-fractalfract-10-00218)\]. Though tree-based ensemble methods (Random Forest, Gradient Boosting Regressor, XGBoost, and so on) are comparatively less flexible in modeling highly intricate relationships, they deliver markedly more stable and reproducible predictions.
The “decomposition–ensemble” system effectively handles the complexity of financial time series and has shown promising results in previous studies. Standard decomposition algorithms include Empirical Mode Decomposition (EMD), Variational Mode Decomposition (VMD), and Wavelet Transform (WT) \[[28](https://www.mdpi.com/2504-3110/10/4/218#B28-fractalfract-10-00218)\]. By decomposing complex time series into components of different frequencies, predicting each component separately, and then aggregating the results, the prediction accuracy for cryptocurrency prices can be significantly improved. However, the existing “decomposition–ensemble” systems decompose the entire financial data sample before splitting it into training and test sets, leading to potential data leakage, as the training set may already include information from the test set \[[29](https://www.mdpi.com/2504-3110/10/4/218#B29-fractalfract-10-00218)\].
As a data preprocessing and feature extraction method, Empirical Mode Decomposition (EMD) still demonstrates its unique superiority in many complex time series prediction tasks. When combined with deep learning models such as LSTM, EMD not only enhances the interpretability of data but also optimizes the prediction accuracy of the model, especially in the fields of stock market prediction, seasonality, and chaotic time series analysis \[[1](https://www.mdpi.com/2504-3110/10/4/218#B1-fractalfract-10-00218),[30](https://www.mdpi.com/2504-3110/10/4/218#B30-fractalfract-10-00218),[31](https://www.mdpi.com/2504-3110/10/4/218#B31-fractalfract-10-00218)\]. Compared to alternative decomposition methods such as VMD and Wavelet Transform, EMD is fully data-driven and requires no prior assumptions, making it particularly suitable for the adaptive, multi-scale analysis of non-stationary financial series. Its balance of interpretability, adaptability, and computational efficiency offers a distinct advantage in modeling complex cryptocurrency returns \[[32](https://www.mdpi.com/2504-3110/10/4/218#B32-fractalfract-10-00218)\]. Therefore, EMD still has irreplaceable advantages in improving prediction performance and robustness, especially when dealing with complex systems.
Building on previous research, this study explores a key issue: whether a sliding decomposition prediction method that overcomes data leakage can outperform the univariate system in predicting ADA returns. Additionally, we use the dynamic LASSO method to examine whether incorporating time-varying economic and policy factors can further enhance the prediction accuracy of ADA returns. These two aspects have often been overlooked in previous studies but are worth investigating \[[33](https://www.mdpi.com/2504-3110/10/4/218#B33-fractalfract-10-00218)\].
To address the limitations identified in prior research, this study introduces the following innovative improvements. First, to overcome the constraints of traditional econometric models in handling nonlinear and non-stationary series, as well as the inadequacy of machine learning methods in capturing the complex, chaotic nature of cryptocurrency markets, we adopt a decomposition–ensemble framework capable of adapting to multi-scale dynamics. Second, we propose a hybrid framework integrating sliding window EMD with machine learning. This approach eliminates the look-ahead bias inherent in full-sample decomposition, avoids the structural constraints of recurrent networks (e.g., LSTM, GRU) on non-stationary series, and leverages the robustness and efficiency of models to deliver superior forecasting performance. Finally, by embedding LASSO-based dynamic factor selection into the prediction of distinct frequency components, we enhance the economic interpretability and forecasting accuracy of the model, thereby achieving a substantive methodological advancement over existing frameworks.
## 3\. Methodology
This section introduces the framework for the Univariate Prediction System, the Multivariate Prediction System, the “Sliding EMD” prediction system, and the “Sliding EMD–Multi Variables” prediction system. We employ a suite of established machine learning models for these forecasting tasks, including Linear Regression (LR), Support Vector Regression (SVR), Random Forest (RF), Gradient Boosting Regression (GBR), and Extreme Gradient Boosting (XGB). These models were selected for their proven efficacy and computational efficiency in financial forecasting. While deep learning architectures can capture complex patterns, they often demand substantial computational resources, are prone to overfitting and output instability in high-frequency financial data, and may not consistently outperform well-tuned traditional machine learning models in return prediction tasks. In contrast, the chosen ensemble and kernel-based methods provide a robust balance between predictive power, interpretability, and training efficiency, and have been widely validated in prior cryptocurrency and financial time series forecasting studies \[[34](https://www.mdpi.com/2504-3110/10/4/218#B34-fractalfract-10-00218)\]. Additionally, [Appendix A.1](https://www.mdpi.com/2504-3110/10/4/218#secAdot1-fractalfract-10-00218), [Appendix A.2](https://www.mdpi.com/2504-3110/10/4/218#secAdot2-fractalfract-10-00218) and [Appendix A.3](https://www.mdpi.com/2504-3110/10/4/218#secAdot3-fractalfract-10-00218) provides detailed descriptions of the error metrics for prediction comparisons and the performance metrics for investment evaluation.
### 3\.1. Univariate Prediction System
The modeling process for the univariate system is shown in [Figure 1](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-f001). First, a fixed window is set, and the BIC criterion is used to select the optimal lag period. The ADA returns for the corresponding lag period are taken as the univariate input, and the future ADA returns are set as the target variable for fitting. For example, with a fixed window of 800 and an optimal lag period of 2, the training set inputs include data from periods 1 and 2, 2 and 3,…, 798 and 799, and the corresponding training set outputs are 3, 4,…, 800. The model is trained using these input–output pairs. For the test set, the ADA returns for periods 799 and 800 are used as input, and the trained model is used to predict the ADA returns for the 801st period.
**Figure 1.** The modeling process of the Univariate Prediction System. Note: [Figure 1](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-f001), [Figure 2](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-f002), [Figure 3](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-f003) and [Figure 4](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-f004) present the methodological workflow of the proposed forecasting systems and were created by the authors.
**Figure 1.** The modeling process of the Univariate Prediction System. Note: [Figure 1](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-f001), [Figure 2](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-f002), [Figure 3](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-f003) and [Figure 4](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-f004) present the methodological workflow of the proposed forecasting systems and were created by the authors.
**Figure 2.** The modeling process of the Multivariate Prediction System.
**Figure 2.** The modeling process of the Multivariate Prediction System.
**Figure 3.** The modeling process of the “Sliding EMD” system.
**Figure 3.** The modeling process of the “Sliding EMD” system.
**Figure 4.** The modeling process of the “Sliding EMD–Multi Variables” system.
**Figure 4.** The modeling process of the “Sliding EMD–Multi Variables” system.
[Figure A1](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-f0A1), [Figure A2](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-f0A2), [Figure A3](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-f0A3) and [Figure A4](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-f0A4) display the optimal hyperparameters for XGB, SVR, GBR, and RF models over 1199 sliding windows. In the “Sklearn” framework, dynamic hyperparameter selection is performed via grid search for each 800-period window. The results show that, for SVR, the parameter “C” is mainly 0.1, with some instances at 10. For XGB, the “maximum\_depth” is typically 3, with smaller portions at 5 and 7, while the “learning\_rate” is mainly 0.01. For GBR, the “maximum\_depth” is mostly 3, with some at 5 and 7, and the “learning\_rate” is 0.01. For RF, the “min\_samples\_split” is distributed across \[[3](https://www.mdpi.com/2504-3110/10/4/218#B3-fractalfract-10-00218),[5](https://www.mdpi.com/2504-3110/10/4/218#B5-fractalfract-10-00218),[7](https://www.mdpi.com/2504-3110/10/4/218#B7-fractalfract-10-00218)\], and the “maximum\_depth” is mostly 3, with smaller portions at 5 and 7.
### 3\.2. Multivariate Prediction System
The modeling process for the multivariate system is shown in [Figure 2](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-f002). The construction of this system is based on the univariate system, where relevant variables affecting ADA returns are selected for each sliding window. The LASSO method is used for feature selection from seven major categories of variables: macroeconomic variables, social variables, exchange rate variables, competitive variables, financial variables, commodity variables, and policy variables. The regularization parameter λ in LASSO is determined within each window via time series cross-validation, which preserves temporal ordering and selects the value that minimizes the one-step-ahead forecast error on the training segment. Variables with non-zero coefficients are retained, and variables with a LASSO coefficient of 0 are discarded. Then, the fixed window is moved forward by one step, and the LASSO selection is repeated for each window until the prediction is completed. The setting of the sliding window approach can help identify the time-varying characteristics of the impact of these seven variables on ADA returns. Furthermore, the LASSO selection results are incorporated as covariates into the prediction model, which improves prediction efficiency by integrating the economically significant variables, thereby improving prediction accuracy. [Figure A5](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-f0A5), [Figure A6](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-f0A6), [Figure A7](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-f0A7) and [Figure A8](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-f0A8) show the optimal hyperparameters for XGB, SVR, GBR, and RF models applied to the multivariate sliding window over 1199 windows.
### 3\.3. “Sliding EMD” System
The modeling process for the “Sliding EMD” prediction system is shown in [Figure 3](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-f003). For an 800-day fixed window, ADA returns are decomposed using the EMD algorithm into multiple modal components. These components are then adaptively grouped into high-frequency and low-frequency clusters via K-means clustering, which operates on a feature vector comprising the sample entropy of each component. This unsupervised clustering naturally separates components with a higher sample entropy into the high-frequency group and those with a lower sample entropy into the low-frequency group, based on the intrinsic complexity of their temporal patterns. This two-scale separation is grounded in the multi-scale nature of financial markets: high-frequency components capture short-term noise and transient shocks, while low-frequency components reflect long-term trends and persistent economic forces \[[35](https://www.mdpi.com/2504-3110/10/4/218#B35-fractalfract-10-00218)\]. Grouping components into these two distinct regimes allows the model to tailor predictive strategies to different temporal dynamics, thereby enhancing interpretability and forecast accuracy. The BIC criterion is applied to select the optimal lag periods for both components. Predictions for each component are summed to obtain the ADA returns for the 801st day. The window then slides forward, and the EMD and K-means reconstruction process is repeated until predictions are completed. The “Sliding EMD” system addresses data leakage issues seen in previous studies, and K-means clustering offers low computational cost with effective reconstruction results. The high-frequency and low-frequency components can also incorporate additional variables. For machine learning methods, optimal parameter tuning is required for both components. To ensure no future information is used, hyperparameter selection is performed independently within each rolling window: a grid search is conducted on the in-sample data of the current window using walk-forward validation, and the best-performing set is retained to forecast the next out-of-sample point. This process yields two sets of dynamic hyperparameters, one for the high-frequency and one for the low-frequency component, that adapt to local market patterns. [Figure A9](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-f0A9), [Figure A10](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-f0A10), [Figure A11](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-f0A11), [Figure A12](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-f0A12), [Figure A13](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-f0A13), [Figure A14](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-f0A14), [Figure A15](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-f0A15) and [Figure A16](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-f0A16) display these dynamically selected optimal hyperparameters for the XGB, SVR, GBR, and RF models applied to the high-frequency and low-frequency components.
### 3\.4. “Sliding EMD–Multi Variables” System
Building on the “Sliding EMD” framework, the “Sliding EMD–Multi Variables” prediction system incorporates LASSO dynamic factor selection for the high-frequency and low-frequency components obtained from each fixed window decomposition. This allows for information gain at the frequency component level, as shown in [Figure 4](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-f004). After component decomposition, reconstruction, and BIC optimal lag selection within each window, LASSO factor selection is applied to identify economic factors influencing ADA returns. The selected factors and optimal lag periods for each component are then used to predict the future values of both frequency components.
For a fixed window of 800, the ADA returns from periods 1 to 800 are decomposed using EMD, and the high-frequency and low-frequency components are reconstructed using K-means. The lag periods for each component are used for fitting, followed by the LASSO selection of key variables with non-zero coefficients for prediction. The predicted values for both components on the 801st day are then summed to obtain the predicted ADA returns. The window is then moved forward by one step, and the process is repeated. [Figure A17](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-f0A17), [Figure A18](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-f0A18), [Figure A19](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-f0A19), [Figure A20](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-f0A20), [Figure A21](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-f0A21), [Figure A22](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-f0A22), [Figure A23](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-f0A23) and [Figure A24](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-f0A24) show the dynamic optimal hyperparameters for XGB, SVR, GBR, and RF models applied to these components.
## 4\. Data Description
### 4\.1. ADA Price and Returns
The ADA return data cover the period from 13 July 2019 to 31 December 2024. Data frequency is daily, and the total data size is 1999.This period includes significant events such as the U.S.–China trade war, fluctuations in commodity prices, the COVID-19 pandemic, and geopolitical conflicts, which provide support for validating the stability of the forecasting system proposed in this study. All subsequent return calculations are based on the logarithmic difference method, which is formulated as follows:
y t \= ln P t / P t − 1
(1)
[Figure 5](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-f005) shows the daily closing price and return series of ADA (data source: <https://cn.investing.com/crypto/cardano/historical-data>, accessed on 26 January 2026). Before 2021, ADA’s technological development was limited, and its price remained low. In September 2021, a significant upgrade introduced smart contract functionality, attracting investor attention. This coincided with a global cryptocurrency bull market, pushing ADA’s price to a peak of \$3\.10. In 2022, macroeconomic tightening and industry crises caused a 60% market cap reduction, leading ADA’s price to fall to \$0\.25 by year-end, a 92% drop from its peak. In 2023, ADA introduced new technology and partnerships, but U.S. regulatory scrutiny hindered price growth. By 2024, with the approval of cryptocurrency-related financial products (spot ETFs), market confidence returned, and ADA’s price slightly rebounded to \$0\.70.
Historical data show that ADA’s price is susceptible to technological upgrades and industry events. Its high volatility is driven by both technological potential and the inherent risk of the cryptocurrency market. The return series highlights frequent, large fluctuations, indicating a significant uncertainty in ADA’s daily returns. This volatility persists, reflecting the ongoing high risk.
### 4\.2. Seven Key Factors Influencing ADA
This study identifies seven key factors: macroeconomic, financial, commodity, exchange rate, policy, attention, and competition variables. Based on Corbet et al. (2020) \[[36](https://www.mdpi.com/2504-3110/10/4/218#B36-fractalfract-10-00218)\], macroeconomic variables include the U.S. federal funds rate, CPI, unemployment rate, and the global Economic Policy Uncertainty index. Financial variables, as suggested by Sánchez et al. (2024) \[[37](https://www.mdpi.com/2504-3110/10/4/218#B37-fractalfract-10-00218)\], include the S\&P 500, NASDAQ, and VIX indices. Commodity variables, such as metal and energy prices, affect ADA based on Manavi et al. (2020) \[[38](https://www.mdpi.com/2504-3110/10/4/218#B38-fractalfract-10-00218)\], with the CRB index representing commodity market influence. Exchange rate fluctuations like USD/CNY and USD/EUR relate to cryptocurrency volatility, prompting a focus on the exchange rate’s role in predictions. According to Isah et al. (2019) \[[39](https://www.mdpi.com/2504-3110/10/4/218#B39-fractalfract-10-00218)\], policy variables such as U.S. fiscal and monetary policy indices significantly impact ADA. Following Auer et al. (2022) \[[40](https://www.mdpi.com/2504-3110/10/4/218#B40-fractalfract-10-00218)\], the Google search index for key ADA events is used as a measure of attention, with 42 key events tested using Granger causality and synthesized via the GDFM model. The competition variable considers Bitcoin and Ethereum, as De et al. (2023) \[[41](https://www.mdpi.com/2504-3110/10/4/218#B41-fractalfract-10-00218)\] found a competitive relationship among major cryptocurrencies. [Figure 6](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-f006) presents the four outcomes of the subsequent LASSO screening: the NASDAQ Composite Index, S\&P 500 Index, US Monetary Policy Index, and US Fiscal Policy Index.
Exchange rates for USD/CNY, USD/EUR, the S\&P 500, VIX, NASDAQ, federal funds rate, U.S. CPI, and U.S. unemployment data are sourced from the Federal Reserve Economic Data (FRED) website: <https://fred.stlouisfed.org/>, accessed on 26 January 2026. CRB, Bitcoin, and Ethereum data come from the Choice Financial Terminal. The global EPU index, U.S. fiscal policy index, and U.S. monetary policy index are directly downloaded from <https://www.policyuncertainty.com/>, accessed on 26 January 2026.
To ensure temporal consistency and prevent the use of future information, all lower-frequency variables are manually aligned with the daily ADA return series. Specifically, for a given month, the same monthly value is assigned to every trading day within that month. This alignment preserves the chronological order of information and eliminates look-ahead bias, as only data available up to each prediction point are used in the rolling window forecasting process.
### 4\.3. Factor Selection Results Based on Least Absolute Shrinkage and Selection Operator (LASSO)
#### 4\.3.1. Factors in the Multivariate Prediction System
In the multivariate sliding window prediction system described in the methodology section, the LASSO method dynamically selects factors from the seven key variables within each sliding window. Since this system performs less effectively than the “Sliding EMD–Multi Variables” prediction system, only a brief introduction to the factor selection results is provided. [Figure A25](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-f0A25) shows the LASSO dynamic factor selection results. It reveals that, without decomposition, the NASDAQ index is selected in nearly all windows, highlighting its substantial impact on ADA returns. The S\&P 500 is chosen in all windows until June 2023, indicating its comparable predictive importance. The U.S. monetary policy variable mainly contributes between October 2021 and May 2022, and in November 2024. [Figure A26](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-f0A26), [Figure A27](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-f0A27) and [Figure A28](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-f0A28) show the dynamic coefficient plots of the LASSO-selected variables for each window in the multivariate system.
#### 4\.3.2. Factors in the “Sliding EMD–Multi Variables” Prediction System
[Figure 7](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-f007) shows the LASSO dynamic factor selection results for the high-frequency components in the “Sliding EMD–Multi Variables” prediction system. Under the sliding window decomposition, the NASDAQ variable is selected in every window, and the S\&P 500 is frequently selected until June 2023. U.S. monetary policy impacts the high-frequency component, especially before April 2022 and after November 2024, consistent with the multivariate sliding window results. U.S. fiscal policy affects the high-frequency component intermittently in 2021 and 2022. The coefficients for the NASDAQ and S\&P 500 are inversely related: NASDAQ has a positive impact, while the S\&P 500 has a negative one. Fiscal and monetary policy variables mainly have a negative impact, except for monetary policy in 2024, which has a positive effect.
[Figure 8](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-f008) shows the dynamic coefficient plots for the high-frequency factors in the “Sliding EMD–Multi Variables” prediction system. From September 2021 to January 2022, the NASDAQ coefficient is positively correlated with ADA, as the Federal Reserve reduced bond purchases, causing volatility in NASDAQ stocks and increasing the short-term correlation with ADA. During the same period, the S\&P 500 coefficient fluctuates negatively, indicating a weakening correlation with ADA due to concerns about economic recession and a shift away from traditional industries. Monetary policy coefficients show a negative relationship with ADA, reflecting the impact of expected interest rate hikes, which led funds to flow into the U.S. dollar and Treasury bonds.
From May 2022, the NASDAQ coefficient turned negative, while the S\&P 500 coefficient shifted positive, reflecting a decline in technology stock valuations and a rise in traditional industries, which led to a drop in ADA’s price. From January to May 2023, both coefficients are significantly negative due to the Silicon Valley Bank incident, which heightened concerns about financial stability. After May 2023, the NASDAQ coefficient turns slightly positive, reflecting a shift in U.S. Federal Reserve policy and easing expectations, driving both the Nasdaq index and ADA higher. In the second half of 2024, the monetary policy coefficient turns positive as the Federal Reserve signals interest rate cuts due to declining inflation expectations, prompting capital inflows into the cryptocurrency market.
The high-frequency model captures short-term shocks to the ADA market. As a barometer for tech stocks, NASDAQ’s volatility reflects market risk appetite and liquidity expectations, making ADA returns highly sensitive to tech sector sentiment. The S\&P 500’s short-term fluctuations mirror macroeconomic risks and industry volatility, acting as a haven during systemic risk and returning to a risk asset status during liquidity expansion. The persistent negative fiscal policy coefficient reflects the impact of short-term fiscal funds and regulatory risks on ADA, while the dynamic monetary policy coefficient captures shifts in short-term liquidity cycles from tightening to easing.
[Figure 9](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-f009) shows the LASSO dynamic factor selection results for the low-frequency components in the “Sliding EMD–Multi Variables” prediction system. The NASDAQ variable is selected throughout, and the S\&P 500 is frequently selected until June 2023, consistent with the high-frequency results. The factors for the low-frequency components align with those for high-frequency components, with NASDAQ having a positive impact and the S\&P 500 having a negative impact.
[Figure 10](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-f010) shows the dynamic coefficient plots for the low-frequency factors in the “Sliding EMD–Multi Variables” prediction system. From September 2021 to January 2022, the NASDAQ coefficient was significantly positive and linked to the ADA contract technology upgrade. In May 2022, it briefly dropped due to a reduced correlation between tech stocks and cryptocurrencies from interest rate hikes. From September 2022 to early 2023, the coefficient continues to decline. After 2023, the NASDAQ coefficient becomes persistently positive but with a smaller magnitude, indicating a weakening long-term correlation with traditional markets.
The impact of the S\&P 500 on the low-frequency component of ADA returns is more pronounced. From 2021 to 2023, the S\&P 500 coefficient remains significant and negative, but after 2023 it becomes zero, indicating no further impact on ADA returns. As a diversified market index, the S\&P 500 reflects a long-term driving factor that differs from ADA, with the coefficient showing a negative correlation between traditional industries and ADA.
The low-frequency model captures long-term market linkages, with policy shocks transmitted through market indices rather than policy variables. The common trend between U.S. tech stocks and ADA remains stable across cycles. The low-frequency data highlights ADA’s independence from traditional indices, filtering out short-term fluctuations and emphasizing the role of technology and macro events on the NASDAQ coefficient. The negative S\&P 500 coefficient reflects the disconnect between the traditional economy and the cryptocurrency market, showing no correlation or a negative one with traditional economic cycles.
After sliding window decomposition, financial variables have the most significant influence. Policy variables impact high-frequency components but not low-frequency components. Compared to the non-decomposed system, fiscal policy significantly affects ADA after EMD. The high-frequency model focuses on short-term dynamics, while the low-frequency model captures long-term trends in market indices. These variable selections reflect the heterogeneous driving factors across time scales.
## 5\. Empirical Results
This section consists of prediction results, investment results, MCS (Model Confidence Set) tests, and comparisons between the univariate system (System 1), multivariate system (System 2), “Sliding EMD” system (System 3), and “Sliding EMD–Multi Variables” system (System 4). The prediction metrics used include MSE, RMSE, MAE, SMAPE, and DSTAT, which represent the performance of different prediction system models. When predicting ADA returns, it is crucial to emphasize practical applicability, especially the impact on investment decisions. For investment results, metrics such as the average daily returns, maximum drawdown, Sharpe ratio, Sortino ratio, and Calmar ratio are used to evaluate the investment performance changes across different systems. Finally, to comprehensively assess the overall effectiveness of the prediction systems, the MCS test is more appropriate. Therefore, the MCS test is used further to verify the advantages and disadvantages of the four systems. [Table A1](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-t0A1) provides the Univariate Prediction System prediction results, [Section 5.1](https://www.mdpi.com/2504-3110/10/4/218#sec5dot1-fractalfract-10-00218) presents the forecasting results and investment performance of the Multivariate Prediction System, [Section 5.2](https://www.mdpi.com/2504-3110/10/4/218#sec5dot2-fractalfract-10-00218) presents the “Sliding EMD” system prediction results and investment comparison, and [Section 5.3](https://www.mdpi.com/2504-3110/10/4/218#sec5dot3-fractalfract-10-00218) presents the “Sliding EMD–Multi Variables” system prediction results and investment comparison.
### 5\.1. Prediction Results for the Multivariate Prediction System
In the Multivariate Prediction System, the LASSO method is applied to the raw ADA returns series to select dynamic factors with non-zero coefficients for prediction. [Table 1](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-t001) shows the prediction results for the five models under the multivariate, and [Table 2](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-t002) presents the comparison between the Multivariate Prediction System and the Univariate Prediction System. The values in [Table 2](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-t002) represent changes relative to the Univariate Prediction System, where a “–” indicates worse forecast performance and a “+” indicates better forecast performance. It can be seen that, aside from four error metrics in the GBR and XGB models where the Multivariate Prediction System performs better, all other model performances are worse. On average, the five models in the Multivariate Prediction System have worsened by 5.422%, 2.614%, 2.972%, 0.572%, and 13.226% in terms of MSE, RMSE, MAE, SMAPE, and DSTAT, respectively. Therefore, under the Multivariate Prediction System, when decomposition techniques are not used, the performance and investment efficiency after incorporating predictive variables are inferior to those of the Univariate Prediction System. The MCS test results in [Table A2](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-t0A2) also indicate that the Multivariate Prediction System performs worse.
### 5\.2. Prediction Results for the “Sliding EMD” System
In the “Sliding EMD” prediction system, a sliding window EMD, K-means clustering, and five prediction methods are applied, focusing on the multi-scale modal features of ADA returns data.
[Table 3](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-t003) shows the prediction results for the five models under the “Sliding EMD” System. The MSE, RMSE, MAE, SMAPE, and DSTAT for the LR model are 3.53 × 10−4, 0.0188, 0.0134, 1.64, and 0.510, respectively. [Figure 11](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-f011) shows the comparison of this system with the Univariate Prediction System. The closer the comparison index of the radar chart is to the external circle, the better the improvement of the system will be. Assuming the prediction models remain unchanged, except for LR (MAE), XGB (MAE), GBR (MAE), and RF (DSTAT), the error metrics improve due to the sliding window decomposition technique. For instance, compared to System 1, the LR model improved MSE by 0.16%, RMSE by 0.08%, MAE by 0.42%, and SMAPE by 4.65%, and DSTAT remained unchanged. On average, the system improved by 0.828% for MSE, 0.416% for RMSE, 5.234% for SMAPE, and 0.418% for DSTAT.
[Figure 12](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-f012) compares the “Sliding EMD” system with the Multivariate Prediction System. Assuming the prediction models remain unchanged, except for XGB (MAE) and GBR (MSE, MAE), the decomposition technique in this system outperforms the Multivariate Prediction System for all other error metrics. For example, compared to System 2, the LR model improved MSE by 12.77%, RMSE by 6.60%, MAE by 7.23%, SMAPE by 5.62%, and DSTAT by 33.81%. On average, the five models improved by 5.522% for MSE, 3.144% for RMSE, 2.602% for MAE, 5.746% for SMAPE, and 17.616% for DSTAT.
**Figure 12.** Comparison of prediction accuracy between the “Sliding EMD” system and the Multivariate Prediction System. Note: [Figure 11](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-f011), [Figure 12](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-f012), [Figure 13](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-f013) and [Figure 14](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-f014) are plotted by the authors based on the empirical results of this study.
**Figure 12.** Comparison of prediction accuracy between the “Sliding EMD” system and the Multivariate Prediction System. Note: [Figure 11](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-f011), [Figure 12](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-f012), [Figure 13](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-f013) and [Figure 14](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-f014) are plotted by the authors based on the empirical results of this study.
**Figure 13.** Comparison of prediction accuracy between the “Sliding EMD–Multi Variables” system and the “Sliding EMD” system. Note: The radar chart also shows percentage data. The closer to the center of the origin, the smaller the data becomes. The further out the data, the greater the percentage, and the stronger the improvement percentage in the comparison between the two systems.
**Figure 13.** Comparison of prediction accuracy between the “Sliding EMD–Multi Variables” system and the “Sliding EMD” system. Note: The radar chart also shows percentage data. The closer to the center of the origin, the smaller the data becomes. The further out the data, the greater the percentage, and the stronger the improvement percentage in the comparison between the two systems.
**Figure 14.** Daily return comparison for the “Sliding EMD–Multi Variables” system.
**Figure 14.** Daily return comparison for the “Sliding EMD–Multi Variables” system.
The MCS test in [Table 4](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-t004) shows that, when comparing System 3 with System 1, the univariate SVR is the worst, while the LR model in the “Sliding EMD” system performs the best. System 3 has an average ranking of 4.2, compared to 6.8 for System 1. When comparing System 3 with System 2, the SVR model under the Multivariate Prediction System performs the worst, and the GBR model under the Multivariate Prediction System performs the best. System 3 has an average ranking of 4.6, while System 2 has an average ranking of 6.2. Overall, System 3 outperforms both System 1 and System 2, which is consistent with the error metric results. The pure decomposition system outperforms both the non-decomposed and multivariate added prediction systems, proving the full effectiveness of decomposition techniques in ADA prediction.
Additionally, this study compares investment performance across the “Sliding EMD” system, the Multivariate Prediction System, and the Univariate Prediction System. [Table 5](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-t005) presents the daily return comparisons. Compared with System 1, System 3’s models show the following improvements in daily return: LR by 9.00 × 10−5, GBR by 3.63 × 10−4, RF by 5.74 × 10−4, SVR by 2.50 × 10−4, and XGB by 5.43 × 10−4. Compared with System 2, System 3’s models improve by 2.64 × 10−3 (LR), 3.76 × 10−4 (GBR), 1.35 × 10−3 (RF), 2.27 × 10−3 (SVR), and 4.24 × 10−4 (XGB). Overall, System 3 outperforms System 1 by an average of 3.64 × 10−4 and System 2 by an average of 1.412 × 10−3 in daily returns. [Table A3](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-t0A3), [Table A4](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-t0A4), [Table A5](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-t0A5) and [Table A6](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-t0A6) illustrate comparisons of the maximum drawdown ratio, Sharpe ratio, Sortino ratio, and Calmar ratio.
### 5\.3. Prediction Results for the “Sliding EMD–Multi Variables” System
In the “Sliding EMD–Multi Variables” prediction system, this study builds upon the “Sliding EMD” system’s decomposition and reconstruction framework. For each fixed window, the high-frequency and low-frequency components obtained through reconstruction are combined with the non-zero coefficient factors selected by the LASSO model as covariates to assist in prediction. [Table 6](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-t006) shows the prediction results for the five models under this system. [Figure 13](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-f013) compares the results with System 3. For the LR model, the MSE improves by 0.94%, RMSE improves by 0.47%, MAE improves by 0.78%, SMAPE worsens by 2.62%, and DSTAT worsens by 0.73%. In the MSE metric, all models perform better, with an average improvement of 0.687%. The RMSE metric also improves on average by 0.338%. The MAE metric is seen as a disadvantage in GBR and XGB, but the other models show an average improvement of 0.266%. The SMAPE and DSTAT metrics do not surpass System 3. The above analysis indicates that incorporating economic variables into the frequency components in the “Sliding EMD–Multi Variables” system improves ADA return forecasting accuracy compared to the “Sliding EMD” system, albeit by a small margin.
[Figure A29](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-f0A29) shows the comparison with the Multivariate Prediction System. For the LR model, MSE improves by 13.59%, RMSE improves by 7.04%, MAE improves by 7.95%, SMAPE improves by 3.15%, and DSTAT improves by 32.82%. Decomposition technology brings significant improvements to all metrics, with the exception of GBR, which sees a slight decline. On average, the five models show improvements of 6.136% for MSE, 3.174% for RMSE, 2.844% for MAE, 3.154% for SMAPE, and 17.528% for DSTAT.
[Figure A30](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-f0A30) compares the ADA return prediction with the Univariate Prediction System. For the LR model, MSE improves by 1.10%, RMSE improves by 0.55%, MAE improves by 0.36%, SMAPE improves by 2.03%, and DSTAT worsens by 14.06%. Decomposition and multivariate inclusion lead to a slight deterioration in DSTAT, GBR (MAE), SVR (SMAPE), and XGB (MAE), while other models show improvements in MSE, RMSE, MAE, and SMAPE, with average improvements of 1.506% for MSE, 0.754% for RMSE, 0.13% for MAE, and 2.478% for SMAPE.
The MCS test results for System 4 are shown in [Table 7](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-t007). When comparing System 4 with System 1, the SVR model in the univariate system performs the worst, while the LR model in the “Sliding EMD” system performs the best. System 4 has an average ranking of 7, compared to 4 for System 1. When comparing System 4 with System 2, the SVR model in the multivariate system performs the worst, and the LR model performs the best. System 4 has an average ranking of 4.4, while System 2 has an average ranking of 6.6. When comparing System 4 with System 3, the SVR model under the “Sliding EMD” framework performs the worst, and the LR model under the “Sliding EMD–Multi Variables” framework performs the best. System 4 has an average ranking of 5.4, while System 3 has an average ranking of 5.6.
In the investment performance comparison for System 4, [Figure 14](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-f014) shows the daily return metrics. Compared to System 1, except for the LR model, all models in System 4 perform better. The LR model worsens by 2.55 × 10−4, while GBR improves by 1.74 × 10−4, RF improves by 6.32 × 10−4, SVR improves by 4.14 × 10−4, and XGB improves by 2.86 × 10−4, with an average improvement of 2.502 × 10−4. System 4 performs better than System 2 across all five models, with LR improving by 2.29 × 10−3, GBR improving by 1.87 × 10−4, RF improving by 1.41 × 10−3, SVR improving by 2.44 × 10−3, and XGB improving by 1.67 × 10−4, with an average improvement of 1.2988 × 10−3. However, System 4 lags behind System 3, with only RF and SVR improving by 5.80 × 10−5 and 1.64 × 10−4, respectively, resulting in an average decrease of 1.138 × 10−4. [Table A7](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-t0A7), [Table A8](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-t0A8), [Table A9](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-t0A9) and [Table A10](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-t0A10) present the comparisons for the maximum drawdown ratio, Sharpe ratio, Sortino ratio, and Calmar ratio. In terms of the maximum drawdown ratio, System 4 improves by an average of 0.166 compared to System 1, and by an average of 0.439 compared to System 2. For the Sharpe ratio, System 4 improves by an average of 0.114 compared to System 1, and by an average of 1.549 compared to System 2. The Sortino ratio shows an improvement of 0.560 for System 4 compared to System 1, and 3.876 compared to System 2. In the Calmar ratio, System 4 improves by an average of 0.0802 compared to System 1, and by 0.239 compared to System 2.
Based on the overall prediction results, investment outcomes, and MCS tests, the Multivariate Prediction System is inferior to the univariate system, the “Sliding EMD” system outperforms both the Univariate and Multivariate Prediction Systems, and the “Sliding EMD–Multi Variables” system does not show a significant improvement over the “Sliding EMD” system but significantly outperforms both the multivariate and univariate systems.
The advantage of the “Sliding EMD” system highlights the importance of the multi-scale composite system method combining the sliding window EMD and K-means clustering proposed in this study. EMD decomposes the complex ADA return series into components at multiple scales via multi-scale analysis, while the sliding window approach effectively prevents the data leakage inherent in traditional decomposition algorithms and ensures that each prediction step is based on real-time information. K-means clustering then adaptively reorganizes these components within each fixed window into high-frequency and low-frequency elements, enhancing prediction accuracy and enabling the subsequent inclusion of variable effects. System 3 significantly outperforms both the univariate and multivariate systems in prediction accuracy and investment performance, demonstrating that the combination of EMD and K-means clustering can effectively extract insights from the ADA time series and provide more reliable support for investment decisions. [Section 4.3.2](https://www.mdpi.com/2504-3110/10/4/218#sec4dot3dot2-fractalfract-10-00218) identified that U.S. stock market, U.S. fiscal policy, and U.S. monetary policy significantly affect different frequency components of ADA returns. The empirical results also show that the “Sliding EMD–Multi Variables” system delivers a slight improvement in forecasting accuracy compared to the “Sliding EMD” system, demonstrating the impact of these key economic variables.
## 6\. Discussion of ADA Return Prediction Results
In recent years, many studies have combined machine learning with the multi-factor prediction of financial asset prices. However, current studies using decomposition algorithms have data leakage problems, and few use real investment performance to verify the model’s application value. [Table 8](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-t008) compares these studies regarding sliding windows, variables, models, etc.
This section compares the “Sliding EMD–Multi Variables” framework with existing forecasting methods. A key question is whether the sliding window decomposition is better than the traditional univariate decomposition. Xu and Niu (2023) \[[13](https://www.mdpi.com/2504-3110/10/4/218#B13-fractalfract-10-00218)\] found that the multi-step sliding window decomposition has a greater prediction advantage for oil price forecasting than the single-step one. However, the sliding decomposition is still not better than the traditional univariate forecast. Although the sliding window method can prevent data leakage, it also reduces the forecast accuracy. However, these studies rarely apply sliding window decomposition to ADA returns. Our results based on error indicators and MCS tests show that the “Sliding EMD” framework outperforms the traditional Univariate Prediction System in ADA return forecasting. Our research offers practical insights into whether including economic and financial variables improves ADA prediction and elucidates whether decomposition techniques and factor selection can further enhance forecasting accuracy.
The existing decomposition forecasting studies, such as those by Viéitez et al. (2024) \[[29](https://www.mdpi.com/2504-3110/10/4/218#B29-fractalfract-10-00218)\], Buse et al. (2025) \[[43](https://www.mdpi.com/2504-3110/10/4/218#B43-fractalfract-10-00218)\], and Li et al. (2022) \[[28](https://www.mdpi.com/2504-3110/10/4/218#B28-fractalfract-10-00218)\], mainly focus on applying advanced single machine learning algorithms or combined models to different decomposed components to obtain comparative advantages but ignore the impact of combining important economic and financial variables, that is, enhancing forecasts through data-driven approaches. However, studies by Bouri et al. (2021) \[[7](https://www.mdpi.com/2504-3110/10/4/218#B7-fractalfract-10-00218)\], Jiang et al. (2021) \[[15](https://www.mdpi.com/2504-3110/10/4/218#B15-fractalfract-10-00218)\], and Hajek et al. (2023) \[[42](https://www.mdpi.com/2504-3110/10/4/218#B42-fractalfract-10-00218)\] show that macroeconomic indicators, exchange rates, financial markets, commodities, monetary and fiscal policies, and online attention all significantly affect ADA returns. Including these variables can improve forecast accuracy, but few studies do so. In this study, based on the “Sliding EMD” framework, we use the LASSO method to screen factors that affect different frequency domain components of ADA returns within each fixed window and then incorporate these selected factors into the forecasting process. Compared with the “Sliding EMD” system, the “Sliding EMD–Multi Variables” system, which is constructed this way, further reduces the forecast error index. It improves investment performance through a data-driven approach and demonstrates the effectiveness of adding component-level variable effects in a sliding window decomposition framework. To date, ADA return forecasting studies have rarely examined the impact of economic and financial factors, especially within a sliding window decomposition framework. By doing so, our study provides practical insights into whether including economic and financial variables improves ADA forecasts and sheds light on whether decomposition techniques and factor selection can improve forecast accuracy.
Finally, these findings have significant practical value for policymakers, financial institutions, and investors. Policymakers can use the multi-scale composite framework developed in this paper as a macroprudential tool for the cryptocurrency market. For example, among the high-frequency components, US fiscal policy, US monetary policy, NASDAQ index, and S\&P 500 index, all affect ADA returns. Regulators can establish a real-time monitoring system to monitor changes in these economic variables to prevent excessive volatility in ADA prices. For investors, using the “Sliding EMD–Multi Variables” forecasting system can increase daily returns by 3.64 × 10−4 compared to the traditional Univariate Prediction System.
## 7\. Conclusions
The Sliding EMD method and economic variables are critical in predicting ADA coin returns. This study constructs four prediction frameworks to assess their effectiveness: the traditional Univariate Prediction System (System 1), the Multivariate Prediction System (System 2), the “Sliding EMD” prediction system (System 3), and the “Sliding EMD–Multi Variables” prediction system (System 4). The empirical results indicate the following:
(1) Regarding the interpretability of ADA return forecasting, financial and policy variables significantly impact both the original ADA return series and the frequency components extracted through Sliding EMD, exhibiting time-varying effects. U.S. fiscal and monetary policies only affect the high-frequency components, while financial variables such as the S\&P 500 and Nasdaq are significant drivers of both high- and low-frequency ADA returns.
(2) In terms of prediction performance, the constructed Multivariate Prediction System does not improve prediction performance. The “Sliding EMD “ prediction system and the “Sliding EMD–Multi Variables” prediction system frameworks demonstrate improvements over the traditional Univariate Prediction System. Specifically, System 3 improved MSE by 0.16%, RMSE by 0.08%, and SMAPE by 4.65%, with DSTAT being unchanged. System 4 follows closely, with improvements of 1.1% in MSE, 0.55% in RMSE, 0.36% in MAE, and 2.03% in SMAPE. These results indicate that Sliding EMD, combined with economic and financial driving variables at the component level, enhances the prediction of ADA returns.
(3) Based on the comparison of investment performance based on the prediction results, the daily return rate of System 3 is better than that of System 1. Similarly, the daily return rate of System 4 is also better than that of System 1. On average, the daily return rate of System 3 is 3.64 × 10−4 higher than that of System 1; the daily return rate of System 4 is 2.502 × 10−4 higher than that of System 1. These investment results are consistent with the prediction accuracy ranking, highlighting this study’s practical value.
This study innovatively applies sliding Empirical Mode Decomposition to predicting ADA returns. This method can decompose the original price series into intrinsic mode functions of different frequencies, effectively capturing information about different frequencies. At the same time, by correlating key economic and financial variables with varying components of frequency obtained using Sliding EMD, this study revealed for the first time that the impact of economic variables on ADA returns has a significant frequency dependence, and these impacts show time-varying characteristics. This provides a new perspective for understanding the complex driving mechanism of the cryptocurrency market.
The findings of this study have important practical significance and broad application prospects, especially for investors and traders, fund managers and quantitative teams, policymakers, and regulators in the cryptocurrency market. For investors and traders, the “Sliding EMD–Multi Variables” forecasting framework (System 4) provided by the study can be used as a core tool for building more accurate trading strategies. Its significantly improved forecasting accuracy directly translates into potential excess returns, which is of great value to active investors. For fund managers and quantitative teams, the study provides a ready-made forecasting tool (System 4), which reveals the frequency decomposition characteristics of the Cardano yield and its correlation mechanism with the macroeconomy. This provides a theoretical and empirical basis for fund managers to design quantitative strategies and conduct risk management. The improved forecasting accuracy directly translates into potential excess returns. This improvement is of great value to active investors. For policymakers and regulators, the study quantifies the significant impact of macroeconomic policies, especially U.S. fiscal and monetary policies, on the volatility of ADA returns from a short-term perspective. This helps policymakers provide decision-making references for formulating macroprudential regulatory frameworks and risk warning mechanisms.
Despite the current research’s findings, there are limitations and room for improvement in ADA return prediction. The K-means clustering method only divides the components into high-frequency and low-frequency categories. Clustering into more components may yield better results. As the research conclusions show, the machine learning models used in this study demonstrate a varying superiority across different prediction systems, and future research could explore using model averaging and weighted integration to combine the advantages of various models. This study examined the EMD algorithm but did not further test the effectiveness of other algorithms. Future research could explore decomposition algorithms with fixed component numbers (such as VMD and SSA), which remain potential areas for further study. Furthermore, the present framework was validated solely on ADA. Although ADA is a prominent and representative cryptocurrency, future work should extend the analysis to other major digital assets to assess the model’s generalizability across different market structures and volatility regimes.
## Author Contributions
W.Z.: Conceptualization, Formal analysis, Investigation; Z.T.: Formal analysis, Writing—original draft, Investigation; X.Z.: Formal analysis, Writing—original draft, Investigation; Y.C.: Data curation, Software, Writing—review and editing; B.D.: Software, Visualization, Validation. All authors have read and agreed to the published version of the manuscript.
## Funding
This research work was supported by the National Natural Science Foundation of China under Grant No. 72341030.
## Data Availability Statement
The original contributions presented in this study are included in the article and [Appendix A](https://www.mdpi.com/2504-3110/10/4/218#app1-fractalfract-10-00218). Further inquiries can be directed to the corresponding author.
## Conflicts of Interest
The authors declare no conflicts of interest.
## Appendix A
### Appendix A.1. Investment Strategy Design
The prediction results from the four systems discussed in the main text can be applied to the design of quantitative investment strategies and investment performance evaluation to assess the practical application value of the models. Since the prediction target in this project is ADA coin returns, which have directional characteristics, we assume investment in a related ADA coin index. Based on the model’s predictions of the index’s upward or downward movement (represented by 1 and 0), there are four trading scenarios: 0-0 represents no position, 0-1 represents entering a position, 1-0 represents closing a position, and 1-1 represents holding a position. The daily returns of each trading day are calculated to evaluate the investment performance of the four prediction systems.
### Appendix A.2. Evaluation Metrics
There are two categories of evaluation metrics: one for assessing prediction results and the other for the economic evaluation of investment performance. For prediction results, this study uses Mean Absolute Error (MAE), Mean Squared Error (MSE), Root Mean Squared Error (RMSE), Symmetric Mean Absolute Percentage Error (SMAPE), and the Directional Accuracy Statistic (DSTAT). The relevant formulas are shown in Equation (A1). Here, T represents the number of samples in the test set, y t is the true value at time t, y ^ t is the predicted value at time t, and I ( ) is an indicator function that takes the value of 1 when the condition is met; otherwise, it takes the value of 0. The economic evaluation metrics for investment performance include the average daily return, maximum drawdown, Sharpe ratio, Sortino ratio, and Calmar ratio. The formulas for calculating the maximum drawdown, Sharpe ratio, Sortino ratio, and Calmar ratio are shown in Equation (A2). In these formulas, E r p represents the expected return of the asset, r f is the risk-free rate, σ p is the asset volatility, R p , t is the sample return below the risk-free rate, and D i and D j are the asset net values at different times.
M S E \= 1 / T ∑ t \= 1 T y t − y t ^ 2 M A E \= 1 / T ∑ t \= 1 T y t − y t ^ R M S E \= 1 / T ∑ t \= 1 T y t − y t ^ 2 S M A P E \= 1 / T ∑ t \= 1 T y t − y t ^ / y t \+ y t ^ 2 D S T A T \= 1 / T ∑ t \= 1 T a t × 100 % , a t \= I y t y t ^ \> 0
(A1)
s h a r p e \= E r p − r f / σ p s o r t i n o \= E r p − r f 1 / ( T − 1 ) ∑ t \= 1 T R p , t − r f 2 c a l m a r \= ( E r p − r f ) / max\_draw\_down max\_draw\_down \= max D i − D j / D i
(A2)
The reason for selecting the above metrics to evaluate investment performance is as follows: the average daily return reflects the short-term profitability of the investment portfolio, making it easy to compare different strategies; the maximum drawdown reflects the maximum loss from peak to trough during a specific period, serving as an important risk measure for the strategy; the Sharpe ratio measures the excess returns per unit of total risk (including volatility), which is a classic metric for evaluating risk-adjusted returns; the Sortino ratio considers only downside risk, making it more suitable for assessing the investor’s sensitivity to losses; the Calmar ratio measures the excess returns per unit of maximum drawdown and is useful for evaluating long-term investment strategies’ risk-adjusted returns.
### Appendix A.3. Model Confidence Set Test
This research utilizes the Model Confidence Set (MCS) test to evaluate and compare the predictive performance of multiple models within two forecasting systems.
Assume the candidate model set constitutes M 0. The purpose of the MCS test is to identify the Model Confidence Set M 1 − α ∗. M 1 − α ∗ includes all the best models at the confidence level 1 − α. The null hypothesis of the MCS test is
H 0 , M : E d i j , t \= 0 , i , j ∈ M
(A3)
In formula (Equation (A3)), d i j , t \= L i , t − L j , t represents the difference sequence of the loss function values between model i and model j. If the null hypothesis H 0 , M is rejected at the confidence level α, the MCS test will sequentially eliminate the model with the worst prediction accuracy from the model set M. This elimination process will continue until the null hypothesis H 0 , M is no longer rejected at the confidence level α. At this point, the remaining models constitute the Model Confidence Set M 1 − α ∗. If the confidence level α remains unchanged during each step of the elimination process, then M 1 − α ∗ includes the best prediction models based on the 1 − α confidence level.
**Figure A1.** Hyperparameter graph of GBR in univariate system.
**Figure A1.** Hyperparameter graph of GBR in univariate system.
**Figure A2.** Hyperparameter graph of RF in univariate system.
**Figure A2.** Hyperparameter graph of RF in univariate system.
**Figure A3.** Hyperparameter graph of SVR in univariate system.
**Figure A3.** Hyperparameter graph of SVR in univariate system.
**Figure A4.** Hyperparameter graph of XGB in univariate system.
**Figure A4.** Hyperparameter graph of XGB in univariate system.
**Figure A5.** Hyperparameter graph of GBR in multivariate system.
**Figure A5.** Hyperparameter graph of GBR in multivariate system.
**Figure A6.** Hyperparameter graph of RF in multivariate system.
**Figure A6.** Hyperparameter graph of RF in multivariate system.
**Figure A7.** Hyperparameter graph of SVR in multivariate system.
**Figure A7.** Hyperparameter graph of SVR in multivariate system.
**Figure A8.** Hyperparameter graph of XGB in multivariate system.
**Figure A8.** Hyperparameter graph of XGB in multivariate system.
**Figure A9.** Hyperparameter diagram of the high-frequency component of GBR in the “Sliding EMD” system.
**Figure A9.** Hyperparameter diagram of the high-frequency component of GBR in the “Sliding EMD” system.
**Figure A10.** Hyperparameter diagram of the high-frequency component of RF in the “Sliding EMD” system.
**Figure A10.** Hyperparameter diagram of the high-frequency component of RF in the “Sliding EMD” system.
**Figure A11.** Hyperparameter diagram of the high-frequency component of SVR in the “Sliding EMD” system.
**Figure A11.** Hyperparameter diagram of the high-frequency component of SVR in the “Sliding EMD” system.
**Figure A12.** Hyperparameter diagram of the high-frequency component of XGB in the “Sliding EMD” system.
**Figure A12.** Hyperparameter diagram of the high-frequency component of XGB in the “Sliding EMD” system.
**Figure A13.** Hyperparameter diagram of the low-frequency component of GBR in the “Sliding EMD” system.
**Figure A13.** Hyperparameter diagram of the low-frequency component of GBR in the “Sliding EMD” system.
**Figure A14.** Hyperparameter diagram of the low-frequency component of RF in the “Sliding EMD” system.
**Figure A14.** Hyperparameter diagram of the low-frequency component of RF in the “Sliding EMD” system.
**Figure A15.** Hyperparameter diagram of the low-frequency component of SVR in the “Sliding EMD” system.
**Figure A15.** Hyperparameter diagram of the low-frequency component of SVR in the “Sliding EMD” system.
**Figure A16.** Hyperparameter diagram of the low-frequency component of XGB in the “Sliding EMD” system.
**Figure A16.** Hyperparameter diagram of the low-frequency component of XGB in the “Sliding EMD” system.
**Figure A17.** The hyperparameter graph of the GBR high-frequency components of the “Sliding EMD–Multi Variables” system.
**Figure A17.** The hyperparameter graph of the GBR high-frequency components of the “Sliding EMD–Multi Variables” system.
**Figure A18.** The hyperparameter graph of the RF high-frequency components of the “Sliding EMD–Multi Variables” system.
**Figure A18.** The hyperparameter graph of the RF high-frequency components of the “Sliding EMD–Multi Variables” system.
**Figure A19.** The hyperparameter graph of the SVR high-frequency components of the “Sliding EMD–Multi Variables” system.
**Figure A19.** The hyperparameter graph of the SVR high-frequency components of the “Sliding EMD–Multi Variables” system.
**Figure A20.** The hyperparameter graph of the XGB high-frequency components of the “Sliding EMD–Multi Variables” system.
**Figure A20.** The hyperparameter graph of the XGB high-frequency components of the “Sliding EMD–Multi Variables” system.
**Figure A21.** The hyperparameter graph of the GBR low-frequency components of the “Sliding EMD–Multi Variables” system.
**Figure A21.** The hyperparameter graph of the GBR low-frequency components of the “Sliding EMD–Multi Variables” system.
**Figure A22.** The hyperparameter graph of the RF low-frequency components of the “Sliding EMD–Multi Variables” system.
**Figure A22.** The hyperparameter graph of the RF low-frequency components of the “Sliding EMD–Multi Variables” system.
**Figure A23.** The hyperparameter graph of the SVR low-frequency components of the “Sliding EMD–Multi Variables” system.
**Figure A23.** The hyperparameter graph of the SVR low-frequency components of the “Sliding EMD–Multi Variables” system.
**Figure A24.** The hyperparameter graph of the XGB low-frequency components of the “Sliding EMD–Multi Variables” system.
**Figure A24.** The hyperparameter graph of the XGB low-frequency components of the “Sliding EMD–Multi Variables” system.
**Figure A25.** Multivariate system prediction result graph.
**Figure A25.** Multivariate system prediction result graph.
**Figure A26.** The Lasso selection relationship coefficient graph of the multivariable system Nasdaq.
**Figure A26.** The Lasso selection relationship coefficient graph of the multivariable system Nasdaq.
**Figure A27.** The Lasso selection relationship coefficient graph of the multivariable system Sp500.
**Figure A27.** The Lasso selection relationship coefficient graph of the multivariable system Sp500.
**Figure A28.** The Lasso choice relationship coefficient diagram of Us monetary policy in a multivariate system.
**Figure A28.** The Lasso choice relationship coefficient diagram of Us monetary policy in a multivariate system.
**Figure A29.** Comparison of prediction accuracy between the “Sliding EMD-Multi Variables” system and the Multivariate Prediction System.
**Figure A29.** Comparison of prediction accuracy between the “Sliding EMD-Multi Variables” system and the Multivariate Prediction System.
**Figure A30.** Comparison of prediction accuracy between the “Sliding EMD-Multi Variables” system and the Univariate Prediction System.
**Figure A30.** Comparison of prediction accuracy between the “Sliding EMD-Multi Variables” system and the Univariate Prediction System.
**Table A1.** Error index table of univariate system results.
**Table A1.** Error index table of univariate system results.
| | LR | GBR | RF | SVR | XGB |
|---|---|---|---|---|---|
| MSE\_1 | 3\.54 × 10−4 | 3\.62 × 10−4 | 3\.63 × 10−4 | 3\.65 × 10−4 | 3\.60 × 10−4 |
| RMSE\_1 | 0\.0188 | 0\.0190 | 0\.0190 | 0\.0191 | 0\.0190 |
| MAE\_1 | 0\.0134 | 0\.0135 | 0\.0135 | 0\.0136 | 0\.0134 |
| SMAPE\_1 | 1\.72 | 1\.78 | 1\.74 | 1\.64 | 1\.75 |
| DSTAT\_1 | 0\.510 | 0\.489 | 0\.504 | 0\.503 | 0\.493 |
**Table A2.** MCS test result table of multivariate system.
**Table A2.** MCS test result table of multivariate system.
| Index | Comparison\_2&1 | |
|---|---|---|
| T R | T S Q | |
| 1 | SVR\_2 (0.000) | SVR\_2 (0.000) |
| 2 | LR\_2 (0.000) | LR\_2 (0.003) |
| 3 | RF\_2 (0.018) | RF\_2 (0.159 \*) |
| 4 | SVR\_1 (0.061) | SVR\_1 (0.269 \*\*) |
| 5 | RF\_1 (0.186 \*) | RF\_1 (0.377 \*\*) |
| 6 | GBR\_1 (0.288 \*\*) | GBR\_1 (0.448 \*\*) |
| 7 | XGB\_1 (0.377 \*\*) | XGB\_1 (0.530 \*\*) |
| 8 | XGB\_2 (0.564 \*\*) | XGB\_2 (0.676 \*\*) |
| 9 | LR\_1 (0.866 \*\*) | LR\_1 (0.866 \*\*) |
| 10 | GBR\_2 (1.000 \*\*) | GBR\_2 (1.000 \*\*) |
**Note:** \*\* and \* denote statistical significance at the 5% and 10% levels, respectively.
**Table A3.** The result table of Maximum Drawdown Ratio of the “Sliding EMD” system.
**Table A3.** The result table of Maximum Drawdown Ratio of the “Sliding EMD” system.
| Maximum Drawdown Ratio | Comparison\_3&1 | Comparison\_3&2 |
|---|---|---|
| LR | 0\.165 | 0\.629 |
| GBR | 0\.199 | 0\.366 |
| RF | 0\.247 | 0\.519 |
| SVR | 0\.165 | 0\.527 |
| XGB | 0\.198 | 0\.300 |
**Table A4.** The result table of Sharpe Ratio of the “Sliding EMD” system.
**Table A4.** The result table of Sharpe Ratio of the “Sliding EMD” system.
| Sharpe Ratio | Comparison\_3&1 | Comparison\_3&2 |
|---|---|---|
| LR | 0\.0371 | 3\.77 |
| GBR | 0\.297 | 0\.314 |
| RF | 0\.687 | 1\.42 |
| SVR | 0\.239 | 2\.54 |
| XGB | 0\.533 | 0\.413 |
**Table A5.** The Sortino Ratio result table of the “Sliding EMD” system.
**Table A5.** The Sortino Ratio result table of the “Sliding EMD” system.
| Sortino Ratio | Comparison\_3&1 | Comparison\_3&2 |
|---|---|---|
| LR | 0\.0905 | 8\.69 |
| GBR | 0\.764 | 0\.857 |
| RF | 1\.79 | 3\.91 |
| SVR | 0\.665 | 6\.71 |
| XGB | 1\.44 | 1\.17 |
**Table A6.** The Calmar Ratio result table of the “Sliding EMD” system.
**Table A6.** The Calmar Ratio result table of the “Sliding EMD” system.
| Calmar Ratio | Comparison\_3&1 | Comparison\_3&2 |
|---|---|---|
| LR | 0\.0579 | 0\.551 |
| GBR | 0\.128 | 0\.0573 |
| RF | 0\.228 | 0\.330 |
| SVR | 0\.109 | 0\.475 |
| XGB | 0\.230 | 0\.138 |
**Table A7.** The result table of the Maximum Drawdown Ratio of the “Sliding EMD-Multi Variables” system.
**Table A7.** The result table of the Maximum Drawdown Ratio of the “Sliding EMD-Multi Variables” system.
| Maximum Drawdown Ratio | Comparison\_4&1 | Comparison\_4&2 | Comparison\_4&3 |
|---|---|---|---|
| LR | −0.0173 | 0\.447 | −0.182 |
| GBR | 0\.0961 | 0\.264 | −0.102 |
| RF | 0\.277 | 0\.549 | 0\.0299 |
| SVR | 0\.293 | 0\.655 | 0\.128 |
| XGB | 0\.180 | 0\.281 | −0.0181 |
**Table A8.** The result table of Sharpe Ratio of the “Sliding EMD-Multi Variables” system.
**Table A8.** The result table of Sharpe Ratio of the “Sliding EMD-Multi Variables” system.
| Sharpe Ratio | Comparison\_4&1 | Comparison\_4&2 | Comparison\_4&3 |
|---|---|---|---|
| LR | −0.385 | 3\.34 | −0.422 |
| GBR | −0.0500 | 0\.0671 | −0.247 |
| RF | 0\.760 | 1\.50 | 0\.0732 |
| SVR | 0\.470 | 2\.78 | 0\.231 |
| XGB | −0.224 | 0\.0562 | −0.357 |
**Table A9.** The Sortino Ratio result table of the “Sliding EMD-Multi Variables” system.
**Table A9.** The Sortino Ratio result table of the “Sliding EMD-Multi Variables” system.
| Sortino Ratio | Comparison\_4&1 | Comparison\_4&2 | Comparison\_4&3 |
|---|---|---|---|
| LR | −1.12 | 7\.48 | −1.21 |
| GBR | 0\.0465 | 0\.139 | −0.718 |
| RF | 2\.04 | 4\.15 | 0\.250 |
| SVR | 1\.39 | 7\.44 | 0\.726 |
| XGB | 0\.445 | 0\.171 | −0.992 |
**Table A10.** The Calmar Ratio result table of the “Sliding EMD-Multi Variables” system.
**Table A10.** The Calmar Ratio result table of the “Sliding EMD-Multi Variables” system.
| Calmar Ratio | Comparison\_4&1 | Comparison\_4&2 | Comparison\_4&3 |
|---|---|---|---|
| LR | −0.144 | 0\.349 | −0.202 |
| GBR | 0\.0412 | −0.0296 | −0.0868 |
| RF | 0\.252 | 0\.354 | 0\.0242 |
| SVR | 0\.202 | 0\.568 | 0\.0924 |
| XGB | 0\.0498 | −0.0423 | −0.180 |
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**Figure 5.** Figure of the ADA daily closing price and return series.
**Figure 5.** Figure of the ADA daily closing price and return series.
**Figure 6.** The time series graph of the four main variables. Note: [Figure 5](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-f005) and [Figure 6](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-f006) are plotted by the authors based on raw data collected from multiple sources.
**Figure 6.** The time series graph of the four main variables. Note: [Figure 5](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-f005) and [Figure 6](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-f006) are plotted by the authors based on raw data collected from multiple sources.
**Figure 7.** LASSO dynamic factor selection results for high-frequency components. Note: [Figure 7](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-f007), [Figure 8](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-f008), [Figure 9](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-f009) and [Figure 10](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-f010) illustrate the LASSO-based dynamic factor selection results and their time-varying coefficients, and were produced by the authors.
**Figure 7.** LASSO dynamic factor selection results for high-frequency components. Note: [Figure 7](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-f007), [Figure 8](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-f008), [Figure 9](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-f009) and [Figure 10](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-f010) illustrate the LASSO-based dynamic factor selection results and their time-varying coefficients, and were produced by the authors.
**Figure 8.** Dynamic coefficient plot of high-frequency factors in the “Sliding EMD–Multi Variables” prediction system.
**Figure 8.** Dynamic coefficient plot of high-frequency factors in the “Sliding EMD–Multi Variables” prediction system.
**Figure 9.** LASSO dynamic factor plot for low-frequency components.
**Figure 9.** LASSO dynamic factor plot for low-frequency components.
**Figure 10.** Dynamic coefficient plot of low-frequency factors in the “Sliding EMD–Multi Variables” prediction system.
**Figure 10.** Dynamic coefficient plot of low-frequency factors in the “Sliding EMD–Multi Variables” prediction system.
**Figure 11.** Comparison of prediction accuracy between the “Sliding EMD” system and the Univariate Prediction System. Note: The radar chart shows percentage data. The closer to the center of the origin, the smaller the data becomes. The further out the data, the greater the percentage, and the stronger the improvement percentage in the comparison between the two systems.
**Figure 11.** Comparison of prediction accuracy between the “Sliding EMD” system and the Univariate Prediction System. Note: The radar chart shows percentage data. The closer to the center of the origin, the smaller the data becomes. The further out the data, the greater the percentage, and the stronger the improvement percentage in the comparison between the two systems.
**Table 1.** Error metrics for the Multivariate Prediction System.
**Table 1.** Error metrics for the Multivariate Prediction System.
| | LR | GBR | RF | SVR | XGB |
|---|---|---|---|---|---|
| MSE\_2 | 4\.05 × 10−4 | 3\.52 × 10−4 | 3\.71 × 10−4 | 4\.13 × 10−4 | 3\.59 × 10−4 |
| RMSE\_2 | 0\.0201 | 0\.0188 | 0\.0193 | 0\.0203 | 0\.0189 |
| MAE\_2 | 0\.0145 | 0\.0133 | 0\.0136 | 0\.0146 | 0\.0134 |
| SMAPE\_2 | 1\.73 | 1\.74 | 1\.73 | 1\.73 | 1\.74 |
| DSTAT\_2 | 0\.381 | 0\.487 | 0\.447 | 0\.367 | 0\.482 |
**Table 2.** Comparison of the Multivariate Prediction System with the Univariate Prediction System.
**Table 2.** Comparison of the Multivariate Prediction System with the Univariate Prediction System.
| Comparison\_2&1 | LR | GBR | RF | SVR | XGB |
|---|---|---|---|---|---|
| MSE\_21 | −14.46% | 2\.64% | −2.17% | −13.41% | 0\.29% |
| RMSE\_21 | −6.98% | 1\.33% | −1.08% | −6.49% | 0\.15% |
| MAE\_21 | −8.25% | 1\.57% | −0.83% | −7.53% | 0\.18% |
| SMAPE\_21 | −1.03% | 2\.07% | 0\.60% | −5.23% | 0\.73% |
| DSTAT\_21 | −25.26% | −0.26% | −11.35% | −26.97% | −2.29% |
Note: A “−” indicates worse forecast performance.
**Table 3.** Error metrics for the “Sliding EMD” system.
**Table 3.** Error metrics for the “Sliding EMD” system.
| | LR | GBR | RF | SVR | XGB |
|---|---|---|---|---|---|
| MSE\_3 | 3\.53 × 10−4 | 3\.57 × 10−4 | 3\.58 × 10−4 | 3\.62 × 10−4 | 3\.57 × 10−4 |
| RMSE\_3 | 0\.0188 | 0\.0189 | 0\.0189 | 0\.0190 | 0\.0189 |
| MAE\_3 | 0\.0134 | 0\.0135 | 0\.0135 | 0\.0136 | 0\.0135 |
| SMAPE\_3 | 1\.64 | 1\.66 | 1\.64 | 1\.59 | 1\.65 |
| DSTAT\_3 | 0\.510 | 0\.500 | 0\.494 | 0\.504 | 0\.500 |
**Table 4.** MCS test results for the “Sliding EMD” system.
**Table 4.** MCS test results for the “Sliding EMD” system.
| Index | Comparison\_3&1 | Comparison\_3&2 | | |
|---|---|---|---|---|
| | T R | T S Q | T R | T S Q |
| 1 | SVR\_1 (0.168 \*) | SVR\_1 (0.182 \*) | SVR\_2 (0.000) | SVR\_2 (0.000) |
| 2 | RF\_1 (0.255 \*\*) | RF\_1 (0.270 \*\*) | LR\_2 (0.000) | LR\_2 (0.000) |
| 3 | SVR\_3 (0.255 \*\*) | SVR\_3 (0.305 \*\*) | RF\_2 (0.016) | RF\_2 (0.208 \*\*) |
| 4 | GBR\_1 (0.438 \*\*) | GBR\_1 (0.424 \*\*) | SVR\_3 (0.134 \*) | SVR\_3 (0.396 \*\*) |
| 5 | XGB\_1 (0.629 \*\*) | XGB\_1 (0.538 \*\*) | RF\_3 (0.633 \*\*) | RF\_3 (0.657 \*\*) |
| 6 | RF\_3 (0.659 \*\*) | RF\_3 (0.546 \*\*) | GBR\_3 (0.633 \*\*) | GBR\_3 (0.657 \*\*) |
| 7 | GBR\_3 (0.659 \*\*) | GBR\_3 (0.550 \*\*) | XGB\_2 (0.633 \*\*) | XGB\_2 (0.657 \*\*) |
| 8 | XGB\_3 (0.659 \*\*) | XGB\_3 (0.550 \*\*) | XGB\_3 (0.633 \*\*) | XGB\_3 (0.657 \*\*) |
| 9 | LR\_1 (0.868 \*\*) | LR\_1 (0.868 \*\*) | LR\_3 (0.934 \*\*) | LR\_3 (0.934 \*\*) |
| 10 | LR\_3 (1.000 \*\*) | LR\_3 (1.000 \*\*) | GBR\_2 (1.000 \*\*) | GBR\_2 (1.000 \*\*) |
**Note:** In [Table 4](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-t004) and in subsequent tables presenting Model Confidence Set test results, asterisks indicate the following significance levels: \* denotes significance at α = 0.05, and \*\* denotes significance at α = 0.01.
**Table 5.** Daily return comparison for the “Sliding EMD” system.
**Table 5.** Daily return comparison for the “Sliding EMD” system.
| Daily Return | Comparison\_3&1 | Comparison\_3&2 |
|---|---|---|
| LR | 9\.00 × 10−5 | 2\.64 × 10−3 |
| GBR | 3\.63 × 10−4 | 3\.76 × 10−4 |
| RF | 5\.74 × 10−4 | 1\.35 × 10−3 |
| SVR | 2\.50 × 10−4 | 2\.27 × 10−3 |
| XGB | 5\.43 × 10−4 | 4\.24 × 10−4 |
**Table 6.** Error metrics for the “Sliding EMD–Multi Variables” system.
**Table 6.** Error metrics for the “Sliding EMD–Multi Variables” system.
| | LR | GBR | RF | SVR | XGB |
|---|---|---|---|---|---|
| MSE\_4 | 3\.50 × 10−4 | 3\.57 × 10−4 | 3\.56 × 10−4 | 3\.56 × 10−4 | 3\.56 × 10−4 |
| RMSE\_4 | 0\.0187 | 0\.0189 | 0\.0189 | 0\.0189 | 0\.0189 |
| MAE\_4 | 0\.0133 | 0\.0135 | 0\.0135 | 0\.0135 | 0\.0135 |
| SMAPE\_4 | 1\.68 | 1\.68 | 1\.68 | 1\.67 | 1\.69 |
| DSTAT\_4 | 0\.507 | 0\.485 | 0\.504 | 0\.514 | 0\.493 |
**Table 7.** MCS test results for the “Sliding EMD–Multi Variables” system.
**Table 7.** MCS test results for the “Sliding EMD–Multi Variables” system.
| Index | Comparison\_4&1 | Comparison\_4&2 | Comparison\_4&3 | | | |
|---|---|---|---|---|---|---|
| | T R | T S Q | T R | T S Q | T R | T S Q |
| 1 | SVR\_1 (0.105 \*) | SVR\_1 (0.108 \*) | SVR\_2 (0.000) | SVR\_2 (0.000) | SVR\_3 (0.275 \*\*) | SVR\_3 (0.222 \*\*) |
| 2 | RF\_1 (0.312 \*\*) | RF\_1 (0.187 \*) | LR\_2 (0.000) | LR\_2 (0.000) | GBR\_4 (0.309 \*\*) | GBR\_4 (0.327 \*\*) |
| 3 | GBR\_1 (0.312 \*\*) | GBR\_1 (0.253 \*\*) | RF\_2 (0.016) | RF\_2 (0.224 \*\*) | RF\_3 (0.309 \*\*) | RF\_3 (0.327 \*\*) |
| 4 | GBR\_4 (0.312 \*\*) | GBR\_4 (0.283 \*\*) | GBR\_4 (0.188 \*) | GBR\_4 (0.456 \*\*) | XGB\_4 (0.309 \*\*) | XGB\_4 (0.327 \*\*) |
| 5 | XGB\_1 (0.312 \*\*) | XGB\_1 (0.283 \*\*) | XGB\_4 (0.188 \*) | XGB\_4 (0.462 \*\*) | RF\_4 (0.494 \*\*) | RF\_4 (0.327 \*\*) |
| 6 | XGB\_4 (0.312 \*\*) | XGB\_4 (0.283 \*\*) | SVR\_4 (0.351 \*\*) | SVR\_4 (0.518 \*\*) | GBR\_3 (0.494 \*\*) | GBR\_3 (0.327 \*\*) |
| 7 | SVR\_4 (0.312 \*\*) | SVR\_4 (0.283 \*\*) | XGB\_2 (0.351 \*\*) | XGB\_2 (0.518 \*\*) | SVR\_4 (0.494 \*\*) | SVR\_4 (0.327 \*\*) |
| 8 | RF\_4 (0.312 \*\*) | RF\_4 (0.283 \*\*) | RF\_4 (0.351 \*\*) | RF\_4 (0.518 \*\*) | XGB\_3 (0.494 \*\*) | XGB\_3 (0.327 \*\*) |
| 9 | LR\_1 (0.488 \*\*) | LR\_1 (0.488 \*\*) | GBR\_2 (0.997 \*\*) | GBR\_2 (0.997 \*\*) | LR\_3 (0.520 \*\*) | LR\_3 (0.520 \*\*) |
| 10 | LR\_4 (1.000 \*\*) | LR\_4 (1.000 \*\*) | LR\_4 (1.000 \*\*) | LR\_4 (1.000 \*\*) | LR\_4 (1.000 \*\*) | LR\_4 (1.000 \*\*) |
**Note:** In [Table 7](https://www.mdpi.com/2504-3110/10/4/218#fractalfract-10-00218-t007), asterisks indicate the following significance levels: \* denotes significance at α = 0.05, and \*\* denotes significance at α = 0.01.
**Table 8.** Comparison with the most relevant studies.
**Table 8.** Comparison with the most relevant studies.
| | Study (Year) | Method | Sliding Window? | Other Predictive Variables? | Potential Future Data Leakage? | Key Empirical Findings/Investment Implications |
|---|---|---|---|---|---|---|
| **1** | Xu and Niu (2023) \[[13](https://www.mdpi.com/2504-3110/10/4/218#B13-fractalfract-10-00218)\] | EMD/VMD-KNN | Yes | Yes (not enough) | No, sliding ensures real-time updates | Decomposition–reconstruction method helps filter out noise from crude oil price time series, improving the prediction accuracy. |
| **2** | Kim et al. (2021) \[[25](https://www.mdpi.com/2504-3110/10/4/218#B25-fractalfract-10-00218)\] | SVR, RF, XGB | No | Yes (only one type of variable) | Yes, full-sample data used | Combining Blockchain data with machine learning algorithms significantly improves the accuracy of Ethereum price forecasts. Investors can analyze Blockchain data, leading to better entry/exit points in the market. |
| **3** | Fallah et al. (2024) \[[26](https://www.mdpi.com/2504-3110/10/4/218#B26-fractalfract-10-00218)\] | LSTM-GRU | Yes | Yes (not enough) | No, sliding ensures real-time updates | Integrating error correction mechanisms into deep learning models improves the prediction accuracy for cryptocurrency prices. This model can provide more accurate price predictions, reducing risk and enhancing decision-making. |
| **4** | Wang et al. (2023) \[[23](https://www.mdpi.com/2504-3110/10/4/218#B23-fractalfract-10-00218)\] | SVM, GBR | Yes | Yes (only three types of variables) | No, sliding ensures real-time updates | Machine learning models, when combined with both internal and external determinants, can significantly improve the prediction of cryptocurrency volatility. Investors can use these insights to better improve risk management and trading strategies. |
| **5** | Qiu et al. (2025) \[[24](https://www.mdpi.com/2504-3110/10/4/218#B24-fractalfract-10-00218)\] | ARIMA-GARCH-LSTM | Yes | Yes (only three types of variables) | No, sliding ensures real-time updates | The model clustering approach enhances volatility forecasting by combining the strengths of multiple models. Investors can use this approach to gain a more reliable forecast of cryptocurrency volatility. |
| **6** | Zhang et al. (2023) \[[12](https://www.mdpi.com/2504-3110/10/4/218#B12-fractalfract-10-00218)\] | VMD-GRU | Yes | Yes (not enough) | No, sliding ensures real-time updates | The model provides improved accuracy in forecasting oil prices by effectively capturing both short-term and long-term trends in the price movements. This approach offers oil traders and investors a powerful tool for predicting price movements, improving trading strategies and hedging decisions. |
| **7** | Li et al. (2022) \[[28](https://www.mdpi.com/2504-3110/10/4/218#B28-fractalfract-10-00218)\] | LR | No | Yes (enough) | Yes, full-sample data used | The study finds that art pricing can be effectively modeled by considering both historical returns and risk factors. Investors in the art market can use these insights to assess the risk and return potential of artworks at auction. |
| **8** | Hajek et al. (2023) \[[42](https://www.mdpi.com/2504-3110/10/4/218#B42-fractalfract-10-00218)\] | RF-XGB-Gradient Boosting | Yes | Yes (enough) | No, sliding ensures real-time updates | The study demonstrates that investor sentiment can significantly improve the prediction of Bitcoin prices. Investors can predict price trends more accurately by considering both market data and sentiment, leading to better timing for Bitcoin investments. |
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