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When comparing competing forecast methods, a primary concern is the relative accuracy of the methods. Ultimately, how well a forecasting method does is reflected in the residuals (“prediction errors”).

(a) One measure of forecasting accuracy is mean absolute deviation (MAD). As the name suggests, it is a measure of the average size of the prediction errors. For a given set of residuals (et ), where et is the residual for period t and n is the number of available residuals. Compute MAD for the 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 MAD values against the moving-average span values of 1, 2, 3, 4, 5, and 6. Describe the behavior of the MAD values versus the span values. For the butter series, at what moving-average span value is MAD smallest?