Reconsider Prob. 20.7-4. Ben Swanson now has decided to use the exponential smoothing method to forecast future sales of washing machines, but he needs to decide on which smoothing constant to use. Using an initial estimate of 24, apply this method retrospectively to the 12 months of last year with  0.1, 0.2, 0.3, 0.4, and 0.5.

(a) Compare MAD for these five values of the smoothing constant α.

(b) Calculate and compare MSE for these five values of α.

Prob. 20.7-4

Ben Swanson, owner and manager of Swanson's Department Store, has decided to use statistical forecasting to get a better handle on the demand for his major products. However, Ben now needs to decide which forecasting method is most appropriate for each category of product. One category is major household appliances, such as washing machines, which have a relatively stable sales level. Monthly sales of washing machines last year are shown below.

(a) Considering that the sales level is relatively stable, which of the most basic forecasting methods-the last-value method or the averaging method or the moving-average method-do you feel would be most appropriate for forecasting future sales? Why?

(b) Use the last-value method retrospectively to determine what the forecasts would have been for the last 11 months of last year. What is MAD?

(c) Use the averaging method retrospectively to determine what the forecasts would have been for the last 11 months of last year. What is MAD?

(d) Use the moving-average method with n = 3 retrospectively to determine what the forecasts would have been for the last 9 months of last year. What is MAD?

(e) Use their MAD values to compare the three methods. (f) Do you feel comfortable in drawing a definitive conclusion about which of the three forecasting methods should be the most accurate in the future based on these 12 months of data?