Forcastings

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.

(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.

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

Find the composite forecast for month seven based on equal weights

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.