Amanta Appliances sells two styles of refrigerators at more than 50 locations in the Midwest. The first style is a relatively expensive model, whereas the second is a standard, less expensive model. Although weekly demand for these two products is fairly stable from week to week, there is enough variation to concern management at Amanta. There have been relatively unsophisticated attempts to forecast weekly demand, but they haven’t been very successful. Sometimes demand (and the corresponding sales) are lower than forecast, so that inventory costs are high. Other times the forecasts are too low. When this happens and on-hand inventory is not sufficient to meet customer demand, Amanta requires expedited shipments to keep customers happy—and this nearly wipes out Amanta’s profit margin on the expedited units. Profits at Amanta would almost certainly increase if demand could be forecast more accurately.

Data on weekly sales of both products appear in the file C12_02.xlsx. A time series chart of the two sales variables indicates what Amanta management expected—namely, there is no evidence of any upward or downward trends or of any seasonality. In fact, it might appear that each series is an unpredictable sequence of random ups and downs. But is this really true? Is it possible to forecast either series, with some degree of accuracy, with an extrapolation method (where only past values of that series are used to forecast current and future values)? Which method appears to be best? How accurate is it? Also, is it possible, when trying to forecast sales of one product, to somehow incorporate current or past sales of the other product in the forecast model? After all, these products might be “substitute” products, where high sales of one go with low sales of the other, or they might be complementary products, where sales of the two products tend to move in the same direction.