Remarks

• Instead of choosing our smoothing parameters to optimize one-period forecast errors, we could, for example, have chosen to optimize the average absolute percentage error incurred in forecasting total housing starts for the next six months.

• Suppose our time series is sales of a software product and we have conducted a major promotion during June 2000. Assume predicted sales for June 2000 were 20,000 units, but we sold 35,000 units. Then a good guess is that the promotion caused 15,000 extra sales during June. When updating the base, trend, and seasonal indexes, however, we should not put in June 2000 sales of 35,000. We should put in June 2000 sales of our forecast (20,000); otherwise, we will incorrectly bump up our forecasts of future sales. When making a forecast for a future month in which there is a promotion similar to the June promotion, we would just bump up the Winter’s method forecast by using the formula 35,000/20,000=75%!

• If at the end of month t we wanted to forecast sales for the next four quarters, we would simply add f_t,1+f_t,2+f_t,3+f_t,4. If desired, we could choose our smoothing parameters to minimize the absolute percentage error incurred in estimating sales for the next year.