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Winters’ Exponential Smoothing

Lesson #5

Winters’ Exponential Smoothing Method

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Winters’ Exponential Smoothing

Model Introduction• A smoothing technique designed to capture trend and seasonality• Estimates a smoothing equation• Uses the estimated smoothing equation to forecast future values• Method format:

– F(t) = a × X(t)/S(t-p) + (1-a) × [F(t-1) + T(t-1)]– S(t) = b × X(t)/F(t) + (1-b) × S(t-p)– T(t) = g × [F(t)-F(t-1)] + (1-g) × T (t-1)– W(t+m) = [F(t) + m × T (t)] × S(t+m-p)

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Winters’ Exponential Smoothing

Model Details• Method characteristics

– Fits a smoothing equation to data– Estimating a smoothing equation which minimizes the errors

between actual data points and model estimates• When to use method

– Data has trend and seasonality • When not to use

– Data does not exhibits trend or seasonality

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Winters’ Exponential Smoothing

Forecasting Steps1. Set an objective2. Build model3. Evaluate model4. Use model

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Winters’ Exponential Smoothing

Objective Setting• Simpler is better• Winters’ exponential smoothing allows to test whether a smoothing

technique with a trend and seasonality works as a model. Objectives should take that principal under consideration

• Example objectives for E-Commerce Retail Sales (see next slide):– Test if E-Commerce Retail Sales can be fit to a trend and

seasonality exponential smoothing model– If E-Commerce Retail Sales exhibits a statistically significant fit,

review and interpret results– If model looks good, create a forecast based off model

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Winters’ Exponential Smoothing

Example: E-Commerce Retail Sales

1998-07-24 1999-12-06 2001-04-19 2002-09-01 2004-01-14 2005-05-28 2006-10-10 2008-02-22 2009-07-06 2010-11-180

5000

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15000

20000

25000

30000

35000

40000

45000

E-Commerce Retail Sales (Millions of Dollars)

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Winters’ Exponential Smoothing

Build Model• Software finds us the best fit line to the data; minimizing the sum of

squared errors

1998-07-24 2001-04-19 2004-01-14 2006-10-10 2009-07-06 2012-04-01 2014-12-270

5000

10000

15000

20000

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30000

35000

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45000

E-Commerce Retail Sales (Millions of $'s)

Actual Forecast

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Winters’ Exponential Smoothing

Evaluate Model• Descriptive Statistics

– Mean– Variance & Standard Deviation

• Accuracy / Error– SSE– RMSE– MAPE– R2; Adjusted R2

• Statistical Significance– F-Test– P-Value F-Test

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Winters’ Exponential Smoothing

ExampleDescriptive Statistics

• Mean– 19673.68

• Variance– 99993090.28

• Standard Deviation– 9999.65

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Winters’ Exponential Smoothing

ExampleAccuracy / Error

• SSE– 82863394.84

• RMSE– 1439.30

• MAPE– 5%

• R2; Adjusted R2

– 97.9%– 97.8%

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Winters’ Exponential Smoothing

ExampleStatistical Significance

• F-Test– 1704.30

• P-Value F-Test– 0.00

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Winters’ Exponential Smoothing

Compare Multiple Models• Skip this step until have knowledge of multiple methods• Will use accuracy/error statistics to compare multiple models to

find best models

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Winters’ Exponential Smoothing

Use Model

• Understand limitations of model• Answer objectives

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Winters’ Exponential Smoothing

Example• Forecasts

2009-10-01 35774.56

2010-01-01 30645.94

2010-04-01 32229.96

2010-07-01 33925.73

2010-10-01 37987.46

2011-01-01 32512.73

2011-04-01 34163.79

2011-07-01 35931.22

2011-10-01 40200.36

2012-01-01 34379.52

2012-04-01 36097.62

2012-07-01 37936.72