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13.11 Refer to the data of exercise 12.11, showing forecasts of growth rates in U.S. gross national product. Compare the mean squared errors of the two sets of forecasts f4t and f5t. Is either of these conditionally efficient with respect to the others?

13.1 We have analyzed the forecast of Table13.1. Consider now based on these data, the actual and predicted changes in this time series.

(a) (i) Plot a graph of predicted change against actual change.

(ii) Find the sample correlation between predicted change and actual change.

(iii) Fit by least squares the regression of actual change on predicted change.

(b) Compare the results in part (a) with those found in this chapter relating actual and predicted levels.

12.4 The accompanying table shows product sales for six consecutive months and two sets of one-month ahead forecasts of these sales. Also shown are forecast for the seventh month. Assume that both sets of forecasts are unbiased.

T x1 f1t f2t

1 672 649 663
2 653 661 658
3 731 695 711
4 596 643 628
5 618 631 615
6 592 580 602
7 640 613

(a) Find the composite forecast for month seven based on equal weights

(b) Find the composite forecast for month seven based on weights inversely proportional to the sums of squares of the last six sets of forecast errors.

(c) Find the composite forecast for the month seven based on a regression approach using the last six sets of forecasts errors.

##### Solution Summary

The solution finds the composite forecast for month seven based on equal weights. The composite forecasts for the month seven based on a regression approach using the last six sets of forecast errors are given.

##### Solution Preview

12.4 The accompanying table shows product sales for six consecutive months and two sets of one-month ahead forecasts of these sales. Also shown are forecast for the seventh month. Assume that both sets of forecasts are unbiased.

T ...

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