MAD (Exercise 13.46)

measures the average magnitude of the prediction errors, and MSE (Exercise 13.47) measures the average squared magnitude of the prediction errors. To put the prediction errors in perspective, it can be useful to measure the errors in terms of percents. One such measure is mean absolute percentage error (MAPE):


MAPE =|et |yt  n× 100%


where et is the residual for period t, yt is the actual observation for period t, and n is the number of available residuals.

(a) Compute MAPE to the hundredth place for residuals from the 1-week, 2-week, 3-week, 4-week, 5-week, and 6-week moving-average models determined in Exercise 13.45, part (c).

(b) Plot the MAPE values against the moving-average span values of 1, 2, 3, 4, 5, and 6. Describe the behavior of the MAPE values versus the span values. For the `butter series, at what moving-average span value is MAPE smallest?


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