Consider the stylized example of Figure 7.3, in which there is a jump in the mean value. Using the same worksheet as a template, enter the exponential smoothing calculations for these periods. Assume that S1 = 100.
FIGURE 7.3 Moving- Average Calculations in a Stylized Example

a. Take a = 0.2. Calculate the forecasts generated by exponential smoothing, and compute the values of MSE, MAD, and MAPE for periods 10-15.
b. Repeat the calculations in part (a) but with a = 0.6.
c. If we suspect that there might be a jump in the underlying process, which of the two values of a examined in parts (a) and (b) would be preferred?

AI BIC Moving Average Example 1 3 Period 4-week Moving Average Observed A(t) Forecast Error Deviation Percent 6-week Moving Average A(t) Forecast DifferenceDeviation Percent 100 100 100 100 100.00 0% 100 100.00 100.00 0.00 0.00 10 100.00 0% 100 100.00 0.00 0.00 100.00 11 100.00 0% 100.00 0% 100 100.00 0.00 0.00 100.00 0.00 0.00 12 0% 0% 100 100.00 100.00 0.00 0.00 100.00 100.00 0.00 0.00 100 13 100.00 100.00 0.00 0.00 100.00 100.00 0.00 0.00 0% 44% 44% 14 10 180 120.00 100.00 80.00 80.00 113.33 100.00 80.00 80.00 15 33% 126.67 66.67 37% 11 180 140.00 120.00 60.00 60.00 113.33 66.67 16 180 22% 30% 12 160.00 140.00 40.00 40.00 140.00 126.67 53.33 53.33 20.00 17 13 180 180.00 160.00 20.00 11% 153.33 140.00 40.00 40.00 22% 18 0% 26.67 15% 14 180 180.00 180.00 0.00 0.00 166.67 153.33 26.67 0% 180.00 166.67 7% 19 15 180 180.00 180.00 0.00 0.00 13.33 13.33 0% 20 180 0.00 0% 16 180.00 180.00 0.00 180.00 180.00 0.00 0.00 21 17 180 180.00 180.00 0.00 0.00 0% 180.00 180.00 0.00 0.00 0% 22 0% 0% 18 180 180.00 180.00 0.00 0.00 180.00 180.00 0.00 0.00 0.00 0% 23 19 180 180.00 180.00 0.00 0.00 0% 180.00 180.00 0.00 24 0% 0% 20 180 180.00 180.00 0.00 0.00 180.00 180.00 0.00 0.00 25 26 MAPE MSE MAPE MSE MAD MAD 27 18.5% 25.9% For periods 10-15 2000.00 33.33 2696.30 46.67 Lon. 7.3 7.2