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Session 8

Session 8. Overview. Forecasting Methods Exponential Smoothing Simple Trend (Holt’s Method) Seasonality (Winters’ Method) Regression Trend Seasonality Lagged Variables. Forecasting. Analysis of Historical Data Time Series (Extrapolation) Regression (Causal)

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Session 8

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  1. Session 8

  2. Overview Forecasting Methods • Exponential Smoothing • Simple • Trend (Holt’s Method) • Seasonality (Winters’ Method) • Regression • Trend • Seasonality • Lagged Variables Applied Regression -- Prof. Juran

  3. Forecasting • Analysis of Historical Data • Time Series (Extrapolation) • Regression (Causal) • Projecting Historical Patterns into the Future • Measurement of Forecast Quality Applied Regression -- Prof. Juran

  4. Measuring Forecasting Errors • Mean Absolute Error • Mean Absolute Percent Error • Root Mean Squared Error • R-square Applied Regression -- Prof. Juran

  5. Mean Absolute Error Applied Regression -- Prof. Juran

  6. e n å i Y = 1 i i = 100 % * MAPE n e n å i ˆ Y = 1 i i = 100 % * Or, alternatively n Mean Absolute Percent Error Applied Regression -- Prof. Juran

  7. Root Mean Squared Error Applied Regression -- Prof. Juran

  8. R-Square Applied Regression -- Prof. Juran

  9. 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 Applied Regression -- Prof. Juran

  10. Example: Revenues at GM Applied Regression -- Prof. Juran

  11. You can right-click on the data series, and choose to superimpose a trend line on the graph: Applied Regression -- Prof. Juran

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  18. You can also show moving-average trend lines, although showing the equation and R-square are no longer options: Applied Regression -- Prof. Juran

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  21. Simple Exponential Smoothing Applied Regression -- Prof. Juran

  22. Why is it called “exponential”? See p. 918 in W&A for more details. Applied Regression -- Prof. Juran

  23. Example: GM Revenue Applied Regression -- Prof. Juran

  24. 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. Applied Regression -- Prof. Juran

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  26. We use Solver to minimize RMSE by manipulating alpha. After optimizing, we see that alpha is 0.350 (instead of 0.10). This makes an improvement in RMSE, from 4691 to 3653. Applied Regression -- Prof. Juran

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  28. Exponential Smoothing with Trend:Holt’s Method Weighted Current Level Weighted Current Observation Weighted Current Trend Applied Regression -- Prof. Juran

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  30. Holt’s model with optimized smoothing constants. This model is slightly better than the simple model (RMSE drops from 3653 to 3568). Applied Regression -- Prof. Juran

  31. Exponential Smoothing with Seasonality:Winters’ Method Applied Regression -- Prof. Juran

  32. Weighted Current Seasonal Factor Weighted Seasonal Factor from Last Year Applied Regression -- Prof. Juran

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  34. Winters’ model with optimized smoothing constants. This model is better than the simple model and the Holt’s model (as measured by RMSE). Applied Regression -- Prof. Juran

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  36. Forecasting with Regression Applied Regression -- Prof. Juran

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  39. Which Method is Better? 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). Applied Regression -- Prof. Juran

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  42. 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. Applied Regression -- Prof. Juran

  43. Lagged Variables • Only applicable in a causal model • Effects of independent variables might not be felt immediately • Used for advertising’s effect on sales Applied Regression -- Prof. Juran

  44. Example: Motel Chain Applied Regression -- Prof. Juran

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