Session 10a

Decision Models -- Prof. Juran2 Overview Forecasting Methods Exponential Smoothing –Simple –Trend (Holt’s Method) –Seasonality (Winters’ Method) Regression –Trend –Seasonality –Lagged Variables

Decision Models -- Prof. Juran3 Forecasting 1.Analysis of Historical Data Time Series (Extrapolation) Regression (Causal) 2.Projecting Historical Patterns into the Future 3.Measurement of Forecast Quality

Decision Models -- Prof. Juran4 Measuring Forecasting Errors Mean Absolute Error Mean Absolute Percent Error Root Mean Squared Error R-square

Decision Models -- Prof. Juran5 Mean Absolute Error

Decision Models -- Prof. Juran6 Mean Absolute Percent Error MAPE  *%100 n Y n i i i   1  Or, alternatively  *%100 n Y n i i i   1 ˆ 

Decision Models -- Prof. Juran7 Root Mean Squared Error

Decision Models -- Prof. Juran8 R -Square

Decision Models -- Prof. Juran9 Trend Analysis Part of the variation in Y is believed to be “explained” by the passage of time Several convenient models available in an Excel chart

Decision Models -- Prof. Juran10 Example: Revenues at GM

Decision Models -- Prof. Juran11 Right-click on the data series Superimpose a trend line on the graph:

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Decision Models -- Prof. Juran17 You can also show moving-average trend lines, although showing the equation and R -square are no longer options:

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Decision Models -- Prof. Juran20 Simple Exponential Smoothing

Decision Models -- Prof. Juran21 Why is it called “exponential”?

Decision Models -- Prof. Juran22 Example: GM Revenue

Decision Models -- Prof. Juran23 In this spreadsheet model, the forecasts appear in column G. Note that our model assumes that there is no trend. We use a default alpha of 0.10.

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Decision Models -- Prof. Juran25 We use Solver to minimize RMSE by manipulating alpha. After optimizing, we see that alpha is (instead of 0.10). This makes an improvement in RMSE, from 4691 to 3653.

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Decision Models -- Prof. Juran27 Exponential Smoothing with Trend: Holt’s Method Weighted Current Trend Weighted Current Observation Weighted Current Level

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Decision Models -- Prof. Juran29 Holt’s model with optimized smoothing constants. This model is slightly better than the simple model ( RMSE drops from 3653 to 3568).

Decision Models -- Prof. Juran30 Exponential Smoothing with Seasonality: Winters’ Method

Decision Models -- Prof. Juran31 Weighted Current Seasonal Factor Weighted Seasonal Factor from Last Year

Decision Models -- Prof. Juran32 Winters’ model with optimized smoothing constants. This model is better than the simple model and the Holt’s model (as measured by RMSE ).

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Decision Models -- Prof. Juran34 Forecasting with Regression

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Decision Models -- Prof. Juran37 The most reasonable statistic for comparison is probably RMSE for smoothing models vs. standard error for regression models, as is reported here: The regression models are superior most of the time (6 out of 10 revenue models and 7 out of 10 EPS models). Which Method is Better?

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Decision Models -- Prof. Juran40 Time series characterized by relatively consistent trends and seasonality favor the regression model. If the trend and seasonality are not stable over time, then Winters’ method does a better job of responding to their changing patterns.

Decision Models -- Prof. Juran41 Lagged Variables Only applicable in a causal model Effects of independent variables might not be felt immediately Used for advertising’s effect on sales

Decision Models -- Prof. Juran42 Example: Motel Chain

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Decision Models -- Prof. Juran49 Here are measures of model fit for the non-regression models: The regression model has a standard error of only 213, which is much better than any of the other models.

Decision Models -- Prof. Juran50 Summary Forecasting Methods Exponential Smoothing –Simple –Trend (Holt’s Method) –Seasonality (Winters’ Method) Regression –Trend –Seasonality –Lagged Variables