The Four Squares Company has used exponential smoothing as a forecasting technique for several years and has established the optimal “weight” to be 0.85. The company’s forecast value for sales last quarter was $1,265 million, and actual sales were $1,385 million.

(a) Derive a forecast of the current quarter’s sales using their exponential smoothing model.

(b) Does the size of the optimal weight tell you anything about the pattern of their sales? Can you deduce why they would get better forecasts by using a relatively heavy weight like this, rather than weighting the most recent observation less heavily?

(c) For what type of data pattern would a time-series decomposition model give better forecasts than an exponential smoothing model?

(d) What kind of data pattern would cause a simple moving-average model to give better fore¬ casts than an exponential smoothing model?