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Calculated Shard: 150 (from laksa080)

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curl -X POST \
  'http://laksa150.int.ahrefs:8124/' \
  -H 'Content-Type: text/plain' \
  -H 'X-ClickHouse-Database: crawler3' \
  -H 'Authorization: Basic YXBpOg==' \
  -d 'SELECT getAhrefsURLFromUnparsed(src_unparsed) AS found_url, ifNull(toUnixTimestamp(download_stamp), 0) AS crawl_time, ifNull(toUnixTimestamp(props_url_first_seen), 0) AS first_indexed_time, download_http_code AS http_code, src_unparsed AS src_unparsed, src_root_hash AS src_root_hash, history_drop_reason AS history_drop_reason, meta_title AS meta_title, meta_descriptions AS meta_descriptions, attrs_boilerpipe_text AS attrs_boilerpipe_text, attrs_markdown AS attrs_markdown, attrs_readable_markdown AS attrs_readable_markdown, meta_canonical AS meta_canonical FROM crawler3.page_info_local FINAL PREWHERE (src_root_hash, src_unparsed) IN ((getAhrefsRootHashFromUnparsed(getAhrefsUnparsedNoserviceFromURL(\'https://www.statisticshowto.com/exponential-smoothing/\')), getAhrefsUnparsedNoserviceFromURL(\'https://www.statisticshowto.com/exponential-smoothing/\'))) FORMAT JSONEachRow'

Response:

{"found_url":"https:\/\/www.statisticshowto.com\/exponential-smoothing\/","crawl_time":1775470089,"first_indexed_time":1585957093,"http_code":200,"src_unparsed":"com,statisticshowto!www,\/exponential-smoothing\/ s443","src_root_hash":"12746512124316119150","history_drop_reason":null,"meta_title":"Exponential Smoothing: Definition of Simple, Double and Triple - Statistics How To","meta_descriptions":["Simple definition of exponential smoothing. Includes single, double, and exponential smoothing (Holt-Winters) methods, with formulas."],"attrs_boilerpipe_text":"Time Series Analysis\n> Exponential Smoothing\nContents:\nWhat is Exponential Smoothing?\nExponential Smoothing in Excel 2016-2013\nExponential smoothing\nof\ntime series\ndata assigns exponentially decreasing weights for newest to oldest\nobservations\n. In other words, the older the data, the less priority (“weight”) the data is given; newer data is seen as more relevant and is assigned more weight. Smoothing parameters (smoothing constants)— usually denoted by α— determine the weights for observations.\nExponential smoothing is usually used to make short term forecasts, as longer term forecasts using this technique can be quite unreliable.\nSimple (single) exponential smoothing\nuses a weighted moving average with exponentially decreasing weights.\nHolt’s trend-corrected double exponential smoothing\nis usually more reliable for handling data that shows\ntrends\n, compared to the single procedure.\nTriple exponential smoothing\n(also called the Multiplicative Holt-Winters) is usually more reliable for parabolic trends or data that shows trends\nand\nseasonality\n..\n1. Simple Exponential Smoothing\nThe\nbasic formula\nis:\nS\nt\n= αy\nt-1\n+ (1 – α) S\nt-1\nWhere\n:\nα = the smoothing constant, a value from 0 to 1. When α is close to zero, smoothing happens more slowly. Following this, the best value for α is the one that results in the smallest\nmean squared error (MSE)\n. Various ways exist to do this, but a popular method is the\nLevenberg–Marquardt algorithm\n.\nt = time period.\nMany alternative formulas exist\n. For example, Roberts (1959) replaced y\nt-1\nwith the current observation, y\nt\n. Another formula uses the forecast for the previous period and current period:\nWhere\n:\nFt – 1 = forecast for the previous period,\nAt – 1 = Actual demand for the period,\na = weight (between 0 and 1). The closer to zero, the smaller the weight.\nWhich formula to use\nis usually a moot point, as most exponential smoothing is performed using software. Whichever formula you use though, you’ll have to set an initial observation. This is a judgment call. You could use an\naverage\nof the first few observations, or you could set the second smoothed value equal to the original observation value to get the ball rolling.\n2. Double Exponential Smoothing\nThis method is deemed more reliable for analyzing data that shows a trend. In addition, this is a more complicated method which adds a second equation to the procedure:\nb\nt\n= γ(S\nt\n– S\nt-1\n) + (1 – γ)b\nt-1\nWhere\n:\nγ is a constant that is chosen with reference to α. Like α it can be chosen through the\nLevenberg–Marquardt algorithm\n.\n3. Triple Exponential Smoothing\nIf your data shows a trend\nand\nseasonality\n, use triple exponential smoothing. In addition to the equations for single and double smoothing, a third equation is used to handle the seasonality aspect:\nI\nt\n= Β y\nt\n\/S\nt\n+ (1-Β)I\nt-L+m\nWhere\n:\ny = observation,\nS = smoothed observation,\nb = trend factor,\nI = seasonal index,\nF = forecast\nm\nperiods ahead,\nt = time period.\nLike α and γ, the optimal Β minimizes the MSE.\nExponential Smoothing in Excel 2016 & 2013\nExponential Smoothing in Excel 2016 & 2013: Overview\nExponential smoothing is a way to smooth out data for presentations or to make forecasts. It’s usually used for finance and economics. If you have a time series with a clear pattern, you could use\nmoving averages\n— but if you don’t have a clear pattern you\ncan\nuse exponential smoothing to forecast.\nDamping Factors\nPerhaps one of the most confusing aspects of exponential smoothing is the\ndamping factor\n. Damping factors are used to smooth out the graph and take on a value between 0 and 1. Technically, the damping factor is 1 minus the\nalpha level\n(1 – α). But all you really need to know is smaller alpha levels (i.e. larger damping factors), smooths out the peaks and valleys more than larger alpha levels (smaller damping factors). Smaller damping factors also mean that your smoothed values are closer to the actual data points than larger damping factors. The easiest way to create exponential smoothing in Excel is to use the\nData Analysis Toolpak\n.\nExponential Smoothing in Excel 2016 & 2013: Steps\nStep 1:\nClick the “Data” tab and then click “Data Analysis.”\nStep 2:\nSelect “Exponential Smoothing” and then click “OK.”\nStep 3:\nClick the Input Range box and then type the location for your forecast data. For example, if you typed your data into cells E1 to E10, type “E1:E10” into that box\nStep 4:\nType a damping factor into the damping factor box. A valid value is 0 to 1. Don’t worry if you aren’t sure what damping factor to type in>you can easily repeat the tests with different damping factors (i.e. 0.9, 0.5, 0.3) to see which one works best.\nStep 5:\nType a cell location into the Output range box. You generally want this in the next column. For example, if you typed your data into cells E1 to E10, type “F1” into that box\nStep 6:\nClick “OK.”\nThe following graph shows the original data set (first column of data), and what happens when a damping factor is applied:\nOriginal data (blue) compared with smoothed data (orange).\nCheck out our\nYouTube channel\nfor more Excel help and tips!\nReferences\nAgresti A. (1990)\nCategorical Data Analysis.\nJohn Wiley and Sons, New York.\nGonick, L. (1993).\nThe Cartoon Guide to Statistics\n. HarperPerennial.\nKotz, S.; et al., eds. (2006),\nEncyclopedia of Statistical Sciences\n, Wiley.\nWheelan, C. (2014).\nNaked Statistics\n. W. W. Norton & Company","attrs_markdown":"[Skip to content](https:\/\/www.statisticshowto.com\/exponential-smoothing\/#content \"Skip to content\")\n\n[Statistics How To](https:\/\/www.statisticshowto.com\/)\n\nMenu\n\n- [Home](https:\/\/www.statisticshowto.com\/)\n- [Tables](https:\/\/www.statisticshowto.com\/tables\/)\n  - [Binomial Distribution Table](https:\/\/www.statisticshowto.com\/tables\/binomial-distribution-table\/)\n  - [F Table](https:\/\/www.statisticshowto.com\/tables\/f-table\/)\n  - [Inverse T Distribution Table](https:\/\/www.statisticshowto.com\/tables\/inverse-t-distribution-table\/)\n  - [PPMC Critical Values](https:\/\/www.statisticshowto.com\/tables\/ppmc-critical-values\/)\n  - [T-Distribution Table (One Tail and Two-Tails)](https:\/\/www.statisticshowto.com\/tables\/t-distribution-table\/)\n  - [Chi Squared Table (Right Tail)](https:\/\/www.statisticshowto.com\/tables\/chi-squared-table-right-tail\/)\n  - [Z-table (Right of Curve or Left)](https:\/\/www.statisticshowto.com\/tables\/z-table\/)\n- [Probability and Statistics](https:\/\/www.statisticshowto.com\/probability-and-statistics\/)\n  - 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[Interquartile Range Calculator](https:\/\/www.statisticshowto.com\/calculators\/interquartile-range-calculator\/)\n  - [Linear Regression Calculator](https:\/\/www.statisticshowto.com\/calculators\/linear-regression-calculator\/)\n  - [Expected Value Calculator](https:\/\/www.statisticshowto.com\/calculators\/expected-value-calculator\/)\n  - [Binomial Distribution Calculator](https:\/\/www.statisticshowto.com\/calculators\/binomial-distribution-calculator\/)\n- [Matrices](https:\/\/www.statisticshowto.com\/matrices-and-matrix-algebra\/)\n- [Experimental Design](https:\/\/www.statisticshowto.com\/experimental-design\/)\n- [Calculus Based Statistics](https:\/\/www.statisticshowto.com\/probability-and-statistics\/calculus-based-statistics\/)\n\n# Exponential Smoothing: Definition of Simple, Double and Triple\n[Time Series Analysis](https:\/\/www.statisticshowto.com\/timeplot\/) \\> Exponential Smoothing\n\n**Contents:**  \n [What is Exponential Smoothing?](https:\/\/www.statisticshowto.com\/exponential-smoothing\/#definition)  \n [Exponential Smoothing in Excel 2016-2013](https:\/\/www.statisticshowto.com\/exponential-smoothing\/#excel)\n\n## What is Exponential Smoothing?\n**Exponential smoothing** of [time series](https:\/\/www.statisticshowto.com\/timeplot\/) data assigns exponentially decreasing weights for newest to oldest [observations](https:\/\/www.statisticshowto.com\/observation-in-statistics\/). In other words, the older the data, the less priority (“weight”) the data is given; newer data is seen as more relevant and is assigned more weight. Smoothing parameters (smoothing constants)— usually denoted by α— determine the weights for observations.\n\nExponential smoothing is usually used to make short term forecasts, as longer term forecasts using this technique can be quite unreliable.\n\n- **Simple (single) exponential smoothing** uses a weighted moving average with exponentially decreasing weights.\n- **Holt’s trend-corrected double exponential smoothing** is usually more reliable for handling data that shows [trends](https:\/\/www.statisticshowto.com\/trend-analysis\/), compared to the single procedure.\n- **Triple exponential smoothing** (also called the Multiplicative Holt-Winters) is usually more reliable for parabolic trends or data that shows trends *and* [seasonality](https:\/\/www.statisticshowto.com\/timeplot\/#seasonality)..\n## 1\\. Simple Exponential Smoothing\nThe **basic formula** is:  \n St = αyt-1 + (1 – α) St-1  \n *Where*:\n\n- α = the smoothing constant, a value from 0 to 1. When α is close to zero, smoothing happens more slowly. Following this, the best value for α is the one that results in the smallest [mean squared error (MSE)](https:\/\/www.statisticshowto.com\/probability-and-statistics\/statistics-definitions\/mean-squared-error\/). Various ways exist to do this, but a popular method is the [Levenberg–Marquardt algorithm](https:\/\/www.statisticshowto.com\/levenberg-marquardt-algorithm\/).\n- t = time period.\n\n**Many alternative formulas exist**. For example, Roberts (1959) replaced yt-1 with the current observation, yt. Another formula uses the forecast for the previous period and current period:  \n [![exponential smoothing formula](https:\/\/www.statisticshowto.com\/wp-content\/uploads\/2016\/10\/exponential-smoothing-formula.png)](https:\/\/www.statisticshowto.com\/wp-content\/uploads\/2016\/10\/exponential-smoothing-formula.png)  \n   \n*Where*:\n\n- Ft – 1 = forecast for the previous period,\n- At – 1 = Actual demand for the period,\n- a = weight (between 0 and 1). The closer to zero, the smaller the weight.\n\n**Which formula to use** is usually a moot point, as most exponential smoothing is performed using software. Whichever formula you use though, you’ll have to set an initial observation. This is a judgment call. You could use an [average](https:\/\/www.statisticshowto.com\/arithmetic-mean\/) of the first few observations, or you could set the second smoothed value equal to the original observation value to get the ball rolling.\n\n## 2\\. Double Exponential Smoothing\nThis method is deemed more reliable for analyzing data that shows a trend. In addition, this is a more complicated method which adds a second equation to the procedure:\n\n> bt = γ(St – St-1) + (1 – γ)bt-1\n\n*Where*:\n\n- γ is a constant that is chosen with reference to α. Like α it can be chosen through the [Levenberg–Marquardt algorithm](http:\/\/people.duke.edu\/~hpgavin\/ce281\/lm.pdf).\n## 3\\. Triple Exponential Smoothing\nIf your data shows a trend *and* [seasonality](https:\/\/www.statisticshowto.com\/timeplot\/#seasonality), use triple exponential smoothing. In addition to the equations for single and double smoothing, a third equation is used to handle the seasonality aspect:  \n It = Β yt\/St + (1-Β)It-L+m  \n *Where*:\n\n- y = observation,\n- S = smoothed observation,\n- b = trend factor,\n- I = seasonal index,\n- F = forecast *m* periods ahead,\n- t = time period.\n\nLike α and γ, the optimal Β minimizes the MSE.\n\n## Exponential Smoothing in Excel 2016 & 2013\n## Exponential Smoothing in Excel 2016 & 2013: Overview\n[![Exponential Smoothing in Excel 2013 \/ 2016](https:\/\/www.statisticshowto.com\/wp-content\/uploads\/2013\/12\/excel-pivot-table-150x150.jpg)](https:\/\/www.statisticshowto.com\/wp-content\/uploads\/2013\/12\/excel-pivot-table.jpg)Exponential smoothing is a way to smooth out data for presentations or to make forecasts. It’s usually used for finance and economics. If you have a time series with a clear pattern, you could use [moving averages](https:\/\/www.statisticshowto.com\/probability-and-statistics\/statistics-definitions\/moving-average\/) — but if you don’t have a clear pattern you *can* use exponential smoothing to forecast.\n\n## Damping Factors\nPerhaps one of the most confusing aspects of exponential smoothing is the **damping factor**. Damping factors are used to smooth out the graph and take on a value between 0 and 1. Technically, the damping factor is 1 minus the [alpha level](https:\/\/www.statisticshowto.com\/probability-and-statistics\/statistics-definitions\/what-is-an-alpha-level\/) (1 – α). But all you really need to know is smaller alpha levels (i.e. larger damping factors), smooths out the peaks and valleys more than larger alpha levels (smaller damping factors). Smaller damping factors also mean that your smoothed values are closer to the actual data points than larger damping factors. The easiest way to create exponential smoothing in Excel is to use the [Data Analysis Toolpak](https:\/\/www.statisticshowto.com\/excel-data-analysis-toolpak\/).\n\n### Exponential Smoothing in Excel 2016 & 2013: Steps\nStep 1: Click the “Data” tab and then click “Data Analysis.”\n\nStep 2: Select “Exponential Smoothing” and then click “OK.”\n\nStep 3: Click the Input Range box and then type the location for your forecast data. For example, if you typed your data into cells E1 to E10, type “E1:E10” into that box\n\nStep 4: Type a damping factor into the damping factor box. A valid value is 0 to 1. Don’t worry if you aren’t sure what damping factor to type in\\>you can easily repeat the tests with different damping factors (i.e. 0.9, 0.5, 0.3) to see which one works best.\n\nStep 5: Type a cell location into the Output range box. You generally want this in the next column. For example, if you typed your data into cells E1 to E10, type “F1” into that box\n\nStep 6: Click “OK.”\n\nThe following graph shows the original data set (first column of data), and what happens when a damping factor is applied:\n\n[![exponential smoothing excel](https:\/\/www.statisticshowto.com\/wp-content\/uploads\/2013\/12\/excel-exponential-smoothing.png)](https:\/\/www.statisticshowto.com\/wp-content\/uploads\/2013\/12\/excel-exponential-smoothing.png)\n\nOriginal data (blue) compared with smoothed data (orange).\n\nCheck out our [YouTube channel](https:\/\/www.youtube.com\/channel\/UC3p_xMSRy1tQ07_7WFk-yqg) for more Excel help and tips\\!\n\n## References\nAgresti A. (1990) [Categorical Data Analysis.](https:\/\/amzn.to\/2O47MZa) John Wiley and Sons, New York.  \n Gonick, L. (1993). [The Cartoon Guide to Statistics](https:\/\/amzn.to\/3iIKTJ4). HarperPerennial.  \n Kotz, S.; et al., eds. (2006), [Encyclopedia of Statistical Sciences](https:\/\/amzn.to\/38y6UFw), Wiley.  \n Wheelan, C. (2014). [Naked Statistics](https:\/\/amzn.to\/3jXb1As). W. W. Norton & Company\n\n[Z Interval: Simple Definition, Formula & Worked Example](https:\/\/www.statisticshowto.com\/z-interval\/)\n\n[Trend Analysis: Simple Definition, Examples](https:\/\/www.statisticshowto.com\/trend-analysis\/)\n\n**Comments? Need to post a correction?** Please [***Contact Us***](https:\/\/www.statisticshowto.com\/contact\/).\n\nCheck out our **[\"Practically Cheating Statistics Handbook](https:\/\/www.statisticshowto.com\/?page_id=15743&preview=true\")**, which gives you hundreds of easy-to-follow answers in a convenient e-book.\n\n[![Statistics Handbook](https:\/\/www.statisticshowto.com\/wp-content\/uploads\/2024\/06\/BookCoverSHT-1.jpg)![Statistics Handbook](https:\/\/www.statisticshowto.com\/wp-content\/uploads\/2024\/06\/BookCoverSHT-1.jpg)](https:\/\/www.statisticshowto.com\/?page_id=15743&preview=true)\n***\n\n**Readers are calling it suspenseful, haunting, and unforgettable. Check out Stephanie’s debut post-apocalyptic novel — available now on Amazon.**\n\n[![an image of S.E. Glen's book Fallout in Georgia](https:\/\/www.statisticshowto.com\/wp-content\/uploads\/2026\/02\/novel-ad.jpg)![an image of S.E. Glen's book Fallout in Georgia](https:\/\/www.statisticshowto.com\/wp-content\/uploads\/2026\/02\/novel-ad.jpg)](https:\/\/amzn.to\/3LLzICB)\n\nLooking for elementary [**statistics help**](https:\/\/www.statisticshowto.com\/help-with-statistics-equations\/)? You’ve come to the right place. **Statistics How To** has more than 1,000 articles and **videos** for elementary statistics, probability, AP and advanced statistics topics. **Looking for a specific topic?** Type it into the search box at the top of the page.\n\nLatest articles\n\n- [Hedges’ g: Definition, Formula](https:\/\/www.statisticshowto.com\/hedges-g\/)\n- [Kaiser-Meyer-Olkin (KMO) Test for Sampling Adequacy](https:\/\/www.statisticshowto.com\/kaiser-meyer-olkin\/)\n- [Benjamini-Hochberg Procedure](https:\/\/www.statisticshowto.com\/benjamini-hochberg-procedure\/)\n- [Tetrachoric Correlation: Definition, Examples, Formula](https:\/\/www.statisticshowto.com\/tetrachoric-correlation\/)\n- [Random Variable: What is it in Statistics?](https:\/\/www.statisticshowto.com\/random-variable\/)\n- [Maximum Likelihood and Maximum Likelihood Estimation](https:\/\/www.statisticshowto.com\/maximum-likelihood-estimation\/)\n- [What is a Parameter in Statistics?](https:\/\/www.statisticshowto.com\/what-is-a-parameter-in-statistics\/)\n- [Beta Level: Definition & Examples](https:\/\/www.statisticshowto.com\/beta-level\/)\n- [Pairwise Independent, Mutually Independent: Definition, Example](https:\/\/www.statisticshowto.com\/pairwise-independent-mutually\/)\n- [Population Mean Definition, Example, Formula](https:\/\/www.statisticshowto.com\/population-mean\/)\n- [Dispersion \/ Measures of Dispersion: Definition](https:\/\/www.statisticshowto.com\/dispersion\/)\n- [Serial Correlation \/ Autocorrelation: Definition, Tests](https:\/\/www.statisticshowto.com\/serial-correlation-autocorrelation\/)\n\n© 2026 [**Statistics How To**](https:\/\/www.statisticshowto.com\/) \\| [About Us](https:\/\/www.statisticshowto.com\/contact\/) \\| [Privacy Policy](https:\/\/www.statisticshowto.com\/privacy-policy\/) \\| [Terms of Use](https:\/\/www.statisticshowto.com\/terms-of-use\/)","attrs_readable_markdown":"[Time Series Analysis](https:\/\/www.statisticshowto.com\/timeplot\/) \\> Exponential Smoothing\n\n**Contents:**  \n [What is Exponential Smoothing?](https:\/\/www.statisticshowto.com\/exponential-smoothing\/#definition)  \n [Exponential Smoothing in Excel 2016-2013](https:\/\/www.statisticshowto.com\/exponential-smoothing\/#excel)\n\n**Exponential smoothing** of [time series](https:\/\/www.statisticshowto.com\/timeplot\/) data assigns exponentially decreasing weights for newest to oldest [observations](https:\/\/www.statisticshowto.com\/observation-in-statistics\/). In other words, the older the data, the less priority (“weight”) the data is given; newer data is seen as more relevant and is assigned more weight. Smoothing parameters (smoothing constants)— usually denoted by α— determine the weights for observations.\n\nExponential smoothing is usually used to make short term forecasts, as longer term forecasts using this technique can be quite unreliable.\n\n- **Simple (single) exponential smoothing** uses a weighted moving average with exponentially decreasing weights.\n- **Holt’s trend-corrected double exponential smoothing** is usually more reliable for handling data that shows [trends](https:\/\/www.statisticshowto.com\/trend-analysis\/), compared to the single procedure.\n- **Triple exponential smoothing** (also called the Multiplicative Holt-Winters) is usually more reliable for parabolic trends or data that shows trends *and* [seasonality](https:\/\/www.statisticshowto.com\/timeplot\/#seasonality)..\n## 1\\. Simple Exponential Smoothing\nThe **basic formula** is:  \n St = αyt-1 + (1 – α) St-1  \n *Where*:\n\n- α = the smoothing constant, a value from 0 to 1. When α is close to zero, smoothing happens more slowly. Following this, the best value for α is the one that results in the smallest [mean squared error (MSE)](https:\/\/www.statisticshowto.com\/probability-and-statistics\/statistics-definitions\/mean-squared-error\/). Various ways exist to do this, but a popular method is the [Levenberg–Marquardt algorithm](https:\/\/www.statisticshowto.com\/levenberg-marquardt-algorithm\/).\n- t = time period.\n\n**Many alternative formulas exist**. For example, Roberts (1959) replaced yt-1 with the current observation, yt. Another formula uses the forecast for the previous period and current period:  \n [![exponential smoothing formula](https:\/\/www.statisticshowto.com\/wp-content\/uploads\/2016\/10\/exponential-smoothing-formula.png)](https:\/\/www.statisticshowto.com\/wp-content\/uploads\/2016\/10\/exponential-smoothing-formula.png)\n\n*Where*:\n\n- Ft – 1 = forecast for the previous period,\n- At – 1 = Actual demand for the period,\n- a = weight (between 0 and 1). The closer to zero, the smaller the weight.\n\n**Which formula to use** is usually a moot point, as most exponential smoothing is performed using software. Whichever formula you use though, you’ll have to set an initial observation. This is a judgment call. You could use an [average](https:\/\/www.statisticshowto.com\/arithmetic-mean\/) of the first few observations, or you could set the second smoothed value equal to the original observation value to get the ball rolling.\n\n## 2\\. Double Exponential Smoothing\nThis method is deemed more reliable for analyzing data that shows a trend. In addition, this is a more complicated method which adds a second equation to the procedure:\n\n> bt = γ(St – St-1) + (1 – γ)bt-1\n\n*Where*:\n\n- γ is a constant that is chosen with reference to α. Like α it can be chosen through the [Levenberg–Marquardt algorithm](http:\/\/people.duke.edu\/~hpgavin\/ce281\/lm.pdf).\n## 3\\. Triple Exponential Smoothing\nIf your data shows a trend *and* [seasonality](https:\/\/www.statisticshowto.com\/timeplot\/#seasonality), use triple exponential smoothing. In addition to the equations for single and double smoothing, a third equation is used to handle the seasonality aspect:  \n It = Β yt\/St + (1-Β)It-L+m  \n *Where*:\n\n- y = observation,\n- S = smoothed observation,\n- b = trend factor,\n- I = seasonal index,\n- F = forecast *m* periods ahead,\n- t = time period.\n\nLike α and γ, the optimal Β minimizes the MSE.\n\n## Exponential Smoothing in Excel 2016 & 2013\n## Exponential Smoothing in Excel 2016 & 2013: Overview\n[![Exponential Smoothing in Excel 2013 \/ 2016](https:\/\/www.statisticshowto.com\/wp-content\/uploads\/2013\/12\/excel-pivot-table-150x150.jpg)](https:\/\/www.statisticshowto.com\/wp-content\/uploads\/2013\/12\/excel-pivot-table.jpg)Exponential smoothing is a way to smooth out data for presentations or to make forecasts. It’s usually used for finance and economics. If you have a time series with a clear pattern, you could use [moving averages](https:\/\/www.statisticshowto.com\/probability-and-statistics\/statistics-definitions\/moving-average\/) — but if you don’t have a clear pattern you *can* use exponential smoothing to forecast.\n\n## Damping Factors\nPerhaps one of the most confusing aspects of exponential smoothing is the **damping factor**. Damping factors are used to smooth out the graph and take on a value between 0 and 1. Technically, the damping factor is 1 minus the [alpha level](https:\/\/www.statisticshowto.com\/probability-and-statistics\/statistics-definitions\/what-is-an-alpha-level\/) (1 – α). But all you really need to know is smaller alpha levels (i.e. larger damping factors), smooths out the peaks and valleys more than larger alpha levels (smaller damping factors). Smaller damping factors also mean that your smoothed values are closer to the actual data points than larger damping factors. The easiest way to create exponential smoothing in Excel is to use the [Data Analysis Toolpak](https:\/\/www.statisticshowto.com\/excel-data-analysis-toolpak\/).\n\n### Exponential Smoothing in Excel 2016 & 2013: Steps\nStep 1: Click the “Data” tab and then click “Data Analysis.”\n\nStep 2: Select “Exponential Smoothing” and then click “OK.”\n\nStep 3: Click the Input Range box and then type the location for your forecast data. For example, if you typed your data into cells E1 to E10, type “E1:E10” into that box\n\nStep 4: Type a damping factor into the damping factor box. A valid value is 0 to 1. Don’t worry if you aren’t sure what damping factor to type in\\>you can easily repeat the tests with different damping factors (i.e. 0.9, 0.5, 0.3) to see which one works best.\n\nStep 5: Type a cell location into the Output range box. You generally want this in the next column. For example, if you typed your data into cells E1 to E10, type “F1” into that box\n\nStep 6: Click “OK.”\n\nThe following graph shows the original data set (first column of data), and what happens when a damping factor is applied:\n\n[![exponential smoothing excel](https:\/\/www.statisticshowto.com\/wp-content\/uploads\/2013\/12\/excel-exponential-smoothing.png)](https:\/\/www.statisticshowto.com\/wp-content\/uploads\/2013\/12\/excel-exponential-smoothing.png)\n\nOriginal data (blue) compared with smoothed data (orange).\n\nCheck out our [YouTube channel](https:\/\/www.youtube.com\/channel\/UC3p_xMSRy1tQ07_7WFk-yqg) for more Excel help and tips\\!\n\n## References\nAgresti A. (1990) [Categorical Data Analysis.](https:\/\/amzn.to\/2O47MZa) John Wiley and Sons, New York.  \n Gonick, L. (1993). [The Cartoon Guide to Statistics](https:\/\/amzn.to\/3iIKTJ4). HarperPerennial.  \n Kotz, S.; et al., eds. (2006), [Encyclopedia of Statistical Sciences](https:\/\/amzn.to\/38y6UFw), Wiley.  \n Wheelan, C. (2014). [Naked Statistics](https:\/\/amzn.to\/3jXb1As). W. W. Norton & Company","meta_canonical":null}

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Boilerpipe Text	Time Series Analysis > Exponential Smoothing Contents: What is Exponential Smoothing? Exponential Smoothing in Excel 2016-2013 Exponential smoothing of time series data assigns exponentially decreasing weights for newest to oldest observations . In other words, the older the data, the less priority (“weight”) the data is given; newer data is seen as more relevant and is assigned more weight. Smoothing parameters (smoothing constants)— usually denoted by α— determine the weights for observations. Exponential smoothing is usually used to make short term forecasts, as longer term forecasts using this technique can be quite unreliable. Simple (single) exponential smoothing uses a weighted moving average with exponentially decreasing weights. Holt’s trend-corrected double exponential smoothing is usually more reliable for handling data that shows trends , compared to the single procedure. Triple exponential smoothing (also called the Multiplicative Holt-Winters) is usually more reliable for parabolic trends or data that shows trends and seasonality .. 1. Simple Exponential Smoothing The basic formula is: S t = αy t-1 + (1 – α) S t-1 Where : α = the smoothing constant, a value from 0 to 1. When α is close to zero, smoothing happens more slowly. Following this, the best value for α is the one that results in the smallest mean squared error (MSE) . Various ways exist to do this, but a popular method is the Levenberg–Marquardt algorithm . t = time period. Many alternative formulas exist . For example, Roberts (1959) replaced y t-1 with the current observation, y t . Another formula uses the forecast for the previous period and current period: Where : Ft – 1 = forecast for the previous period, At – 1 = Actual demand for the period, a = weight (between 0 and 1). The closer to zero, the smaller the weight. Which formula to use is usually a moot point, as most exponential smoothing is performed using software. Whichever formula you use though, you’ll have to set an initial observation. This is a judgment call. You could use an average of the first few observations, or you could set the second smoothed value equal to the original observation value to get the ball rolling. 2. Double Exponential Smoothing This method is deemed more reliable for analyzing data that shows a trend. In addition, this is a more complicated method which adds a second equation to the procedure: b t = γ(S t – S t-1 ) + (1 – γ)b t-1 Where : γ is a constant that is chosen with reference to α. Like α it can be chosen through the Levenberg–Marquardt algorithm . 3. Triple Exponential Smoothing If your data shows a trend and seasonality , use triple exponential smoothing. In addition to the equations for single and double smoothing, a third equation is used to handle the seasonality aspect: I t = Β y t /S t + (1-Β)I t-L+m Where : y = observation, S = smoothed observation, b = trend factor, I = seasonal index, F = forecast m periods ahead, t = time period. Like α and γ, the optimal Β minimizes the MSE. Exponential Smoothing in Excel 2016 & 2013 Exponential Smoothing in Excel 2016 & 2013: Overview Exponential smoothing is a way to smooth out data for presentations or to make forecasts. It’s usually used for finance and economics. If you have a time series with a clear pattern, you could use moving averages — but if you don’t have a clear pattern you can use exponential smoothing to forecast. Damping Factors Perhaps one of the most confusing aspects of exponential smoothing is the damping factor . Damping factors are used to smooth out the graph and take on a value between 0 and 1. Technically, the damping factor is 1 minus the alpha level (1 – α). But all you really need to know is smaller alpha levels (i.e. larger damping factors), smooths out the peaks and valleys more than larger alpha levels (smaller damping factors). Smaller damping factors also mean that your smoothed values are closer to the actual data points than larger damping factors. The easiest way to create exponential smoothing in Excel is to use the Data Analysis Toolpak . Exponential Smoothing in Excel 2016 & 2013: Steps Step 1: Click the “Data” tab and then click “Data Analysis.” Step 2: Select “Exponential Smoothing” and then click “OK.” Step 3: Click the Input Range box and then type the location for your forecast data. For example, if you typed your data into cells E1 to E10, type “E1:E10” into that box Step 4: Type a damping factor into the damping factor box. A valid value is 0 to 1. Don’t worry if you aren’t sure what damping factor to type in>you can easily repeat the tests with different damping factors (i.e. 0.9, 0.5, 0.3) to see which one works best. Step 5: Type a cell location into the Output range box. You generally want this in the next column. For example, if you typed your data into cells E1 to E10, type “F1” into that box Step 6: Click “OK.” The following graph shows the original data set (first column of data), and what happens when a damping factor is applied: Original data (blue) compared with smoothed data (orange). Check out our YouTube channel for more Excel help and tips! References Agresti A. (1990) Categorical Data Analysis. John Wiley and Sons, New York. Gonick, L. (1993). The Cartoon Guide to Statistics . HarperPerennial. Kotz, S.; et al., eds. (2006), Encyclopedia of Statistical Sciences , Wiley. Wheelan, C. (2014). Naked Statistics . W. W. Norton & Company
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[Matrices](https://www.statisticshowto.com/matrices-and-matrix-algebra/) - [Experimental Design](https://www.statisticshowto.com/experimental-design/) - [Calculus Based Statistics](https://www.statisticshowto.com/probability-and-statistics/calculus-based-statistics/) # Exponential Smoothing: Definition of Simple, Double and Triple [Time Series Analysis](https://www.statisticshowto.com/timeplot/) \> Exponential Smoothing Contents: [What is Exponential Smoothing?](https://www.statisticshowto.com/exponential-smoothing/#definition) [Exponential Smoothing in Excel 2016-2013](https://www.statisticshowto.com/exponential-smoothing/#excel) ## What is Exponential Smoothing? Exponential smoothing of [time series](https://www.statisticshowto.com/timeplot/) data assigns exponentially decreasing weights for newest to oldest [observations](https://www.statisticshowto.com/observation-in-statistics/). In other words, the older the data, the less priority (“weight”) the data is given; newer data is seen as more relevant and is assigned more weight. Smoothing parameters (smoothing constants)— usually denoted by α— determine the weights for observations. Exponential smoothing is usually used to make short term forecasts, as longer term forecasts using this technique can be quite unreliable. - Simple (single) exponential smoothing uses a weighted moving average with exponentially decreasing weights. - Holt’s trend-corrected double exponential smoothing is usually more reliable for handling data that shows [trends](https://www.statisticshowto.com/trend-analysis/), compared to the single procedure. - Triple exponential smoothing (also called the Multiplicative Holt-Winters) is usually more reliable for parabolic trends or data that shows trends and [seasonality](https://www.statisticshowto.com/timeplot/#seasonality).. ## 1\. Simple Exponential Smoothing The basic formula is: St = αyt-1 + (1 – α) St-1 Where: - α = the smoothing constant, a value from 0 to 1. When α is close to zero, smoothing happens more slowly. Following this, the best value for α is the one that results in the smallest [mean squared error (MSE)](https://www.statisticshowto.com/probability-and-statistics/statistics-definitions/mean-squared-error/). Various ways exist to do this, but a popular method is the [Levenberg–Marquardt algorithm](https://www.statisticshowto.com/levenberg-marquardt-algorithm/). - t = time period. Many alternative formulas exist. For example, Roberts (1959) replaced yt-1 with the current observation, yt. Another formula uses the forecast for the previous period and current period: [![exponential smoothing formula](https://www.statisticshowto.com/wp-content/uploads/2016/10/exponential-smoothing-formula.png)](https://www.statisticshowto.com/wp-content/uploads/2016/10/exponential-smoothing-formula.png) Where: - Ft – 1 = forecast for the previous period, - At – 1 = Actual demand for the period, - a = weight (between 0 and 1). The closer to zero, the smaller the weight. Which formula to use is usually a moot point, as most exponential smoothing is performed using software. Whichever formula you use though, you’ll have to set an initial observation. This is a judgment call. You could use an [average](https://www.statisticshowto.com/arithmetic-mean/) of the first few observations, or you could set the second smoothed value equal to the original observation value to get the ball rolling. ## 2\. Double Exponential Smoothing This method is deemed more reliable for analyzing data that shows a trend. In addition, this is a more complicated method which adds a second equation to the procedure: > bt = γ(St – St-1) + (1 – γ)bt-1 Where: - γ is a constant that is chosen with reference to α. Like α it can be chosen through the [Levenberg–Marquardt algorithm](http://people.duke.edu/~hpgavin/ce281/lm.pdf). ## 3\. Triple Exponential Smoothing If your data shows a trend and [seasonality](https://www.statisticshowto.com/timeplot/#seasonality), use triple exponential smoothing. In addition to the equations for single and double smoothing, a third equation is used to handle the seasonality aspect: It = Β yt/St + (1-Β)It-L+m Where: - y = observation, - S = smoothed observation, - b = trend factor, - I = seasonal index, - F = forecast m periods ahead, - t = time period. Like α and γ, the optimal Β minimizes the MSE. ## Exponential Smoothing in Excel 2016 & 2013 ## Exponential Smoothing in Excel 2016 & 2013: Overview [![Exponential Smoothing in Excel 2013 / 2016](https://www.statisticshowto.com/wp-content/uploads/2013/12/excel-pivot-table-150x150.jpg)](https://www.statisticshowto.com/wp-content/uploads/2013/12/excel-pivot-table.jpg)Exponential smoothing is a way to smooth out data for presentations or to make forecasts. It’s usually used for finance and economics. If you have a time series with a clear pattern, you could use [moving averages](https://www.statisticshowto.com/probability-and-statistics/statistics-definitions/moving-average/) — but if you don’t have a clear pattern you can use exponential smoothing to forecast. ## Damping Factors Perhaps one of the most confusing aspects of exponential smoothing is the damping factor. Damping factors are used to smooth out the graph and take on a value between 0 and 1. Technically, the damping factor is 1 minus the [alpha level](https://www.statisticshowto.com/probability-and-statistics/statistics-definitions/what-is-an-alpha-level/) (1 – α). But all you really need to know is smaller alpha levels (i.e. larger damping factors), smooths out the peaks and valleys more than larger alpha levels (smaller damping factors). Smaller damping factors also mean that your smoothed values are closer to the actual data points than larger damping factors. The easiest way to create exponential smoothing in Excel is to use the [Data Analysis Toolpak](https://www.statisticshowto.com/excel-data-analysis-toolpak/). ### Exponential Smoothing in Excel 2016 & 2013: Steps Step 1: Click the “Data” tab and then click “Data Analysis.” Step 2: Select “Exponential Smoothing” and then click “OK.” Step 3: Click the Input Range box and then type the location for your forecast data. For example, if you typed your data into cells E1 to E10, type “E1:E10” into that box Step 4: Type a damping factor into the damping factor box. A valid value is 0 to 1. Don’t worry if you aren’t sure what damping factor to type in\>you can easily repeat the tests with different damping factors (i.e. 0.9, 0.5, 0.3) to see which one works best. Step 5: Type a cell location into the Output range box. You generally want this in the next column. For example, if you typed your data into cells E1 to E10, type “F1” into that box Step 6: Click “OK.” The following graph shows the original data set (first column of data), and what happens when a damping factor is applied: [![exponential smoothing excel](https://www.statisticshowto.com/wp-content/uploads/2013/12/excel-exponential-smoothing.png)](https://www.statisticshowto.com/wp-content/uploads/2013/12/excel-exponential-smoothing.png) Original data (blue) compared with smoothed data (orange). Check out our [YouTube channel](https://www.youtube.com/channel/UC3p_xMSRy1tQ07_7WFk-yqg) for more Excel help and tips\! ## References Agresti A. (1990) [Categorical Data Analysis.](https://amzn.to/2O47MZa) John Wiley and Sons, New York. Gonick, L. (1993). [The Cartoon Guide to Statistics](https://amzn.to/3iIKTJ4). HarperPerennial. Kotz, S.; et al., eds. (2006), [Encyclopedia of Statistical Sciences](https://amzn.to/38y6UFw), Wiley. Wheelan, C. (2014). [Naked Statistics](https://amzn.to/3jXb1As). W. W. Norton & Company [Z Interval: Simple Definition, Formula & Worked Example](https://www.statisticshowto.com/z-interval/) [Trend Analysis: Simple Definition, Examples](https://www.statisticshowto.com/trend-analysis/) Comments? Need to post a correction? Please [*Contact Us](https://www.statisticshowto.com/contact/). Check out our ["Practically Cheating Statistics Handbook](https://www.statisticshowto.com/?page_id=15743&preview=true"), which gives you hundreds of easy-to-follow answers in a convenient e-book. [![Statistics Handbook](https://www.statisticshowto.com/wp-content/uploads/2024/06/BookCoverSHT-1.jpg)![Statistics Handbook](https://www.statisticshowto.com/wp-content/uploads/2024/06/BookCoverSHT-1.jpg)](https://www.statisticshowto.com/?page_id=15743&preview=true) Readers are calling it suspenseful, haunting, and unforgettable. Check out Stephanie’s debut post-apocalyptic novel — available now on Amazon. [![an image of S.E. 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Readable Markdown	[Time Series Analysis](https://www.statisticshowto.com/timeplot/) \> Exponential Smoothing Contents: [What is Exponential Smoothing?](https://www.statisticshowto.com/exponential-smoothing/#definition) [Exponential Smoothing in Excel 2016-2013](https://www.statisticshowto.com/exponential-smoothing/#excel) Exponential smoothing of [time series](https://www.statisticshowto.com/timeplot/) data assigns exponentially decreasing weights for newest to oldest [observations](https://www.statisticshowto.com/observation-in-statistics/). In other words, the older the data, the less priority (“weight”) the data is given; newer data is seen as more relevant and is assigned more weight. Smoothing parameters (smoothing constants)— usually denoted by α— determine the weights for observations. Exponential smoothing is usually used to make short term forecasts, as longer term forecasts using this technique can be quite unreliable. - Simple (single) exponential smoothing uses a weighted moving average with exponentially decreasing weights. - Holt’s trend-corrected double exponential smoothing is usually more reliable for handling data that shows [trends](https://www.statisticshowto.com/trend-analysis/), compared to the single procedure. - Triple exponential smoothing (also called the Multiplicative Holt-Winters) is usually more reliable for parabolic trends or data that shows trends and [seasonality](https://www.statisticshowto.com/timeplot/#seasonality).. ## 1\. Simple Exponential Smoothing The basic formula is: St = αyt-1 + (1 – α) St-1 Where: - α = the smoothing constant, a value from 0 to 1. When α is close to zero, smoothing happens more slowly. Following this, the best value for α is the one that results in the smallest [mean squared error (MSE)](https://www.statisticshowto.com/probability-and-statistics/statistics-definitions/mean-squared-error/). Various ways exist to do this, but a popular method is the [Levenberg–Marquardt algorithm](https://www.statisticshowto.com/levenberg-marquardt-algorithm/). - t = time period. Many alternative formulas exist. For example, Roberts (1959) replaced yt-1 with the current observation, yt. Another formula uses the forecast for the previous period and current period: [![exponential smoothing formula](https://www.statisticshowto.com/wp-content/uploads/2016/10/exponential-smoothing-formula.png)](https://www.statisticshowto.com/wp-content/uploads/2016/10/exponential-smoothing-formula.png) Where: - Ft – 1 = forecast for the previous period, - At – 1 = Actual demand for the period, - a = weight (between 0 and 1). The closer to zero, the smaller the weight. Which formula to use is usually a moot point, as most exponential smoothing is performed using software. Whichever formula you use though, you’ll have to set an initial observation. This is a judgment call. You could use an [average](https://www.statisticshowto.com/arithmetic-mean/) of the first few observations, or you could set the second smoothed value equal to the original observation value to get the ball rolling. ## 2\. Double Exponential Smoothing This method is deemed more reliable for analyzing data that shows a trend. In addition, this is a more complicated method which adds a second equation to the procedure: > bt = γ(St – St-1) + (1 – γ)bt-1 Where: - γ is a constant that is chosen with reference to α. Like α it can be chosen through the [Levenberg–Marquardt algorithm](http://people.duke.edu/~hpgavin/ce281/lm.pdf). ## 3\. Triple Exponential Smoothing If your data shows a trend and [seasonality](https://www.statisticshowto.com/timeplot/#seasonality), use triple exponential smoothing. In addition to the equations for single and double smoothing, a third equation is used to handle the seasonality aspect: It = Β yt/St + (1-Β)It-L+m Where: - y = observation, - S = smoothed observation, - b = trend factor, - I = seasonal index, - F = forecast m periods ahead, - t = time period. Like α and γ, the optimal Β minimizes the MSE. ## Exponential Smoothing in Excel 2016 & 2013 ## Exponential Smoothing in Excel 2016 & 2013: Overview [![Exponential Smoothing in Excel 2013 / 2016](https://www.statisticshowto.com/wp-content/uploads/2013/12/excel-pivot-table-150x150.jpg)](https://www.statisticshowto.com/wp-content/uploads/2013/12/excel-pivot-table.jpg)Exponential smoothing is a way to smooth out data for presentations or to make forecasts. It’s usually used for finance and economics. If you have a time series with a clear pattern, you could use [moving averages](https://www.statisticshowto.com/probability-and-statistics/statistics-definitions/moving-average/) — but if you don’t have a clear pattern you can use exponential smoothing to forecast. ## Damping Factors Perhaps one of the most confusing aspects of exponential smoothing is the damping factor. Damping factors are used to smooth out the graph and take on a value between 0 and 1. Technically, the damping factor is 1 minus the [alpha level](https://www.statisticshowto.com/probability-and-statistics/statistics-definitions/what-is-an-alpha-level/) (1 – α). But all you really need to know is smaller alpha levels (i.e. larger damping factors), smooths out the peaks and valleys more than larger alpha levels (smaller damping factors). Smaller damping factors also mean that your smoothed values are closer to the actual data points than larger damping factors. The easiest way to create exponential smoothing in Excel is to use the [Data Analysis Toolpak](https://www.statisticshowto.com/excel-data-analysis-toolpak/). ### Exponential Smoothing in Excel 2016 & 2013: Steps Step 1: Click the “Data” tab and then click “Data Analysis.” Step 2: Select “Exponential Smoothing” and then click “OK.” Step 3: Click the Input Range box and then type the location for your forecast data. For example, if you typed your data into cells E1 to E10, type “E1:E10” into that box Step 4: Type a damping factor into the damping factor box. A valid value is 0 to 1. Don’t worry if you aren’t sure what damping factor to type in\>you can easily repeat the tests with different damping factors (i.e. 0.9, 0.5, 0.3) to see which one works best. Step 5: Type a cell location into the Output range box. You generally want this in the next column. For example, if you typed your data into cells E1 to E10, type “F1” into that box Step 6: Click “OK.” The following graph shows the original data set (first column of data), and what happens when a damping factor is applied: [![exponential smoothing excel](https://www.statisticshowto.com/wp-content/uploads/2013/12/excel-exponential-smoothing.png)](https://www.statisticshowto.com/wp-content/uploads/2013/12/excel-exponential-smoothing.png) Original data (blue) compared with smoothed data (orange). Check out our [YouTube channel](https://www.youtube.com/channel/UC3p_xMSRy1tQ07_7WFk-yqg) for more Excel help and tips\! ## References Agresti A. (1990) [Categorical Data Analysis.](https://amzn.to/2O47MZa) John Wiley and Sons, New York. Gonick, L. (1993). [The Cartoon Guide to Statistics](https://amzn.to/3iIKTJ4). HarperPerennial. Kotz, S.; et al., eds. (2006), [Encyclopedia of Statistical Sciences](https://amzn.to/38y6UFw), Wiley. Wheelan, C. (2014). [Naked Statistics](https://amzn.to/3jXb1As). W. W. Norton & Company
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