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Combination Forecast Consider the ForecastX" Audit Trail printouts below. They represent and analysis of a combination model for Gap sales using a Winters model and a multiple-regression model. The results of the Winters model are the series Gapsales_WFCST. The results for the multiple-regression model are the series Gapsales_RECST. Regression #1 Audit Trail -- Coefficient Table (Multiple Regression Selected) Included Overall Coefficient Standard T-test F-test Elasticity Series Description in Model F.test Gap Sales (5000) Dependent - 6,467.84 10,332.93 -0.63 0.39 5,005.67 Gapsales RFCST Yes 0.11 0.04 2.60 6.75 0.11 Gapsales_WECST Yes 0.91 0.04 22.58 510.08 0.90 Audit Trail - Statistics Accuracy Measures Value Forecast Statistics Value AIC 1,361.38 Durbin Watson 1.75 BIC 1,363.41 Mean 804,816.13 Mean Absolute Percentage Error (MAPE) 5.21 96 Standard Deviation 628,227.16 Sum Squared Error (SSE) 114,310,689.710.20 Max 3,029,900.00 R-Square 99.47 96 Min 105.715.00 Adjusted R-Square 99.45 % Range 2,924,185.00 Mean Absolute Error 34,833.08 Ljung-Box 0.76 Mean Error 0.00 Mean Square Error 2,041,262,316.25 Root Mean Square Error 45,180.33 Theil 0.27 Coefficient Standard Regression #2 Audit Trail -- Coefficient Table (Multiple Regression Selected) Series Description Included Overall in Model Error T-test F-test Elasticity F-test Gap Sales ($000) Dependent 0.00 0.00 0.00 0.00 5,062.49 Gapsales_RFCST Yes 0.1018 0.04 2.54 6.47 0.00 Gapsales_WFCST Yes 0.9112 0.04 22.70 515.50 0.91 Audit Trail - Statistics Accuracy Measures Value Forecast Statistics Value AIC 1,361.80 Durbin Watson 1.72 BIC 1,363.82 Mean 804,816.13 Mean Absolute Percentage Error (MAPE) 5.08 % Standard Deviation 628,227.16 Sum Squared Error (SSE) 115,155,739,746 Max 3,029,900.00 R-Square 99.47 % Min 105,715.00 Adjusted R-Square 99.45 % Range 2,924,185.00 Mean Absolute Error 34,538.72 Ljung-Box 0.94 Mean Error -2,333.11 Mean Square Error 2,056,352,495.47 Root Mean Square Error 45,347.02 Theil 0.27 Forecast for 1999 Gap Sales Combined Date ($000) Forecast Mar-99 2277700 2,160,500.79 Jun-99 2453300 2,359,986.28 Sep-99 3045386 3,111,234.20 Dec-99 3858939 3,788,377.03 In the preparation of a combination forecast, Regression #1 above is used to determine if the two component models will contribute to the combined model. O is used to determine if each component model has an adequate t-statistic. is used to determine if there is no systematic bias in the two component models. O is used to determine if the Durbin Watson is close to 2. 1. Explain why a combined model might be better than any of the original contributing models. 2. Could there be cases in which a combined model would show no gain in forecast accuracy over the original models? Give an example where this situation might be likely to occur. For the toolbar, press ALT+F10 (PC) or ALT+FN+F10 (Mac). BI U S Paragraph Open Sanssa. 10pt !!! A we Combination Forecast Consider the ForecastX" Audit Trail printouts below. They represent and analysis of a combination model for Gap sales using a Winters model and a multiple-regression model. The results of the Winters model are the series Gapsales_WFCST. The results for the multiple-regression model are the series Gapsales_RECST. Regression #1 Audit Trail -- Coefficient Table (Multiple Regression Selected) Included Overall Coefficient Standard T-test F-test Elasticity Series Description in Model F.test Gap Sales (5000) Dependent - 6,467.84 10,332.93 -0.63 0.39 5,005.67 Gapsales RFCST Yes 0.11 0.04 2.60 6.75 0.11 Gapsales_WECST Yes 0.91 0.04 22.58 510.08 0.90 Audit Trail - Statistics Accuracy Measures Value Forecast Statistics Value AIC 1,361.38 Durbin Watson 1.75 BIC 1,363.41 Mean 804,816.13 Mean Absolute Percentage Error (MAPE) 5.21 96 Standard Deviation 628,227.16 Sum Squared Error (SSE) 114,310,689.710.20 Max 3,029,900.00 R-Square 99.47 96 Min 105.715.00 Adjusted R-Square 99.45 % Range 2,924,185.00 Mean Absolute Error 34,833.08 Ljung-Box 0.76 Mean Error 0.00 Mean Square Error 2,041,262,316.25 Root Mean Square Error 45,180.33 Theil 0.27 Coefficient Standard Regression #2 Audit Trail -- Coefficient Table (Multiple Regression Selected) Series Description Included Overall in Model Error T-test F-test Elasticity F-test Gap Sales ($000) Dependent 0.00 0.00 0.00 0.00 5,062.49 Gapsales_RFCST Yes 0.1018 0.04 2.54 6.47 0.00 Gapsales_WFCST Yes 0.9112 0.04 22.70 515.50 0.91 Audit Trail - Statistics Accuracy Measures Value Forecast Statistics Value AIC 1,361.80 Durbin Watson 1.72 BIC 1,363.82 Mean 804,816.13 Mean Absolute Percentage Error (MAPE) 5.08 % Standard Deviation 628,227.16 Sum Squared Error (SSE) 115,155,739,746 Max 3,029,900.00 R-Square 99.47 % Min 105,715.00 Adjusted R-Square 99.45 % Range 2,924,185.00 Mean Absolute Error 34,538.72 Ljung-Box 0.94 Mean Error -2,333.11 Mean Square Error 2,056,352,495.47 Root Mean Square Error 45,347.02 Theil 0.27 Forecast for 1999 Gap Sales Combined Date ($000) Forecast Mar-99 2277700 2,160,500.79 Jun-99 2453300 2,359,986.28 Sep-99 3045386 3,111,234.20 Dec-99 3858939 3,788,377.03 In the preparation of a combination forecast, Regression #1 above is used to determine if the two component models will contribute to the combined model. O is used to determine if each component model has an adequate t-statistic. is used to determine if there is no systematic bias in the two component models. O is used to determine if the Durbin Watson is close to 2. 1. Explain why a combined model might be better than any of the original contributing models. 2. Could there be cases in which a combined model would show no gain in forecast accuracy over the original models? Give an example where this situation might be likely to occur. For the toolbar, press ALT+F10 (PC) or ALT+FN+F10 (Mac). BI U S Paragraph Open Sanssa. 10pt !!! A we