Prompt: 10.24

The choice of the smoothing constants,and , has a considerable effect on the accuracy of the forecasts obtained by using exponential smoothing with trend.

For each of the following time series, set= 0.2 and then compare MAD obtained with = 0.1, 0.2, 0.3, 0.4,and 0.5. Begin with initial estimates of 50 for the average value and 2 for the trend.

1. 52, 55, 55, 58, 59, 63, 64, 66, 67, 72, 73, 74
2. 52, 55, 59, 61, 66, 69, 71, 72, 73, 74, 73, 74
3. 52, 53, 51, 50, 48, 47, 49, 52, 57, 62, 69, 74

Step 1) Change the Beta Value and a graph for each of the 5 given Beta values in each of the 3 databases. one graph per tab with 5 separate lines. The graphs is already part of the spreadsheet for the beta value

Step 2) the impact of the Beta value on the 3 databases.

Template for Exponential Smoothing Forecasting Method with Trend Exponential Range Name Cells Alpha J6 Time True Latest Estimated Smoothing Forecasting Beta 17 Period Value Trend Trend Forecast Error Smoothing Constants Estimated Trend E6:E35 a = B = Forecast F6:F35 #VALUE! Forecasting Error G6:G35 Initial Estimates InitialEstimateAverage J10 Average = InitialEstimate Trend J11 Trend = LatestTrend D6:D35 MAD J14 Mean Absolute Deviation MSE J17 W N J OO OO VOULAWN MAD = #DIV/O! True Value C6:C35 Mean Square Error MSE = #DIV/O! 14 15 16 17 18 19 20 21 -+ True Value 22 23 Value Forecast 24 25 ooo 0 - 26 27 28 29 30 O 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 Time Period 10.24a 10.24b 10.24c +Template for Exponential Smoothing Forecasting Method with Trend Exponential Range Name Cells Alpha 16 Time True Latest Estimated Smoothing Forecasting Trend Error J7 Forecast Beta Period Value Trend Smoothing Constants Estimated Trend E6:E35 #VALUE! B = Forecast F6:F35 Forecasting Error G6:G35 Initial Estimates InitialEstimateAverage J10 Average = InitialEstimate Trend J11 Trend = LatestTrend D6:D35 MAD J14 N = 3 6 0 V O U A W N Mean Absolute Deviation MSE J17 MAD = #DIV/O! True Value C6:C35 Mean Square Error MSE = #DIV/O! 19 20 22 + True Value 23 Value Forecast o - 24 25 26 27 28 oo 29 30 O 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 Time Period 10.24a 10.24b 10.24c +Template for Exponential Smoothing Forecasting Method with Trend Exponential Range Name Cells J6 Time True Latest Estimated Smoothing Forecasting Alpha Period Value Trend Trend Forecast Error Smoothing Constants Beta J7 0 a = Estimated Trend E6:E35 #VALUE! B = Forecast F6:F35 Forecasting Error G6:G35 Initial Estimates InitialEstimateAverage J10 Average = InitialEstimate Trend J11 Trend = LatestTrend D6:D35 MAD J14 Mean Absolute Deviation MSE J17 MAD = #DIV/O! True Value C6:C35 O JI A W N T OO OO V O U A W N Mean Square Error MSE = #DIV/O! 17 18 19 20 21 22 True Value 23 Value Forecast 24 25 26 27 booo 28 29 30 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 Time Period 10.24a 10.24b 10.24c +