Reconsider the sales data for a certain product given in Prob. 27.5-4. The company’s management now has decided to discontinue incorporating seasonal effects into its forecasting procedure for this product because there does not appear to be a substantial seasonal pattern. Management also is concerned that exponential smoothing may not be the best forecasting method for this product and so has decided to test and compare several forecasting methods. Each method is to be applied retrospectively to the given data and then its MSE is to be calculated. The method with the smallest value of MSE will be chosen to begin forecasting. Apply this retrospective test and calculate MSE for each of the following methods. (Also obtain the forecast for the upcoming quarter with each method.)
T(a) The moving-average method based on the last four quarters, so start with a forecast for the fifth quarter.
T(b) The exponential smoothing method with α = 0.1. Start with a forecast for the third quarter by using the sales for the second quarter as the latest observation and the sales for the first quarter as the initial estimate.
T(c) The exponential smoothing method with α = 0.3. Start as described in part (b).
T(d) The exponential smoothing with trend method with α = 0.3 and β = 0.3. Start with a forecast for the third quarter by using the sales for the second quarter as the initial estimate of the expected value of the time series (A) and the difference (sales for second quarter minus sales for first quarter) as the initial estimate of the trend of the time series (B).
(e) Compare MSE for these methods. Which one has the smallest value of MSE?