Management of the Jackson Manufacturing Corporation wishes to choose a statistical forecasting method for forecasting total sales for the corporation. Total sales (in millions of dollars) for each month of last year are shown below.

(a) Note how the sales level is shifting significantly from month to month-first trending upward and then dipping down before resuming an upward trend. Assuming that similar patterns would continue in the future, evaluate how well you feel each of the five forecasting methods introduced in Secs. 20.4 and 20.6 would perform in forecasting future sales.

(b) Apply the last-value method, the averaging method, and the moving-average method (with n = 3) retrospectively to last year's sales and compare their MAD values.

(c) Using an initial estimate of 120, apply the exponential smoothing method retrospectively to last year's sales with  0.1, 0.2, 0.3, 0.4, and 0.5. Compare MAD for these five values of the smoothing constant α.

(d) Using initial estimates of 120 for the expected value and 10 for the trend, apply exponential smoothing with trend retrospectively to last year's sales. Use all combinations of the smoothing constants where α = 0.1 or 0.3 or 0.5 and ß = 0.1 or 0.3 or 0.5. Compare MAD for these nine combinations.

(e) Which one of the above forecasting methods would you recommend that management use? Using this method, what is the forecast of total sales for January of the new year?