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Session 10a

Session 10a. 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 10a

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  1. Session 10a

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

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

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

  5. Mean Absolute Error Decision Models -- Prof. Juran

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

  7. Root Mean Squared Error Decision Models -- Prof. Juran

  8. R-Square Decision Models -- 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 Decision Models -- Prof. Juran

  10. Example: Revenues at GM Decision Models -- Prof. Juran

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

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  21. Simple Exponential Smoothing Decision Models -- Prof. Juran

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

  23. Example: GM Revenue Decision Models -- 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. Decision Models -- 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. Decision Models -- Prof. Juran

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

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

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

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

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  35. Forecasting with Regression Decision Models -- Prof. Juran

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  38. 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). Decision Models -- Prof. Juran

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  41. 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. Juran

  42. 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. Juran

  43. Example: Motel Chain Decision Models -- Prof. Juran

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  50. 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. Juran

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