The models of this chapter emphasize forecasting the level of a series. For many business decisions, forecasts of change are more important. If we’re projecting an increase in sales, then we need to...

The models of this chapter emphasize forecasting the level of a series. For many business decisions, forecasts of change are more important. If we’re projecting an increase in sales, then we need to have more items in stock. This timeplot shows sales (in thousands of dollars) over a 25-week period (not including special holiday sales).

(a) The following output summarizes the fit of an AR(2) model to these data. Assuming that the model meets the usual conditions, is this a good description of the dependence in this series?

(b) If we use the same two predictors
 and
 to describe the changes in sales or use the differences
, what will be the estimated slopes for the lagged variables?

(c) Explain why
 of the regression of
 on these two lags is the same as the SD of the residuals when regressing the changes on these two lags.

(d) Although the models are equivalent (in the sense that you can get the slope for one from the other), most analysts prefer to fit models to
 itself rather than to the differences. A partial explanation comes from a comparison of
 for the two models. Which model do you think has a larger
: the model with
 as the response, or the model with the differences
? (Hint: Both models leave the same variance in the residuals, but one has more variance in the response.)