Suppose that the researcher decided to determine the stability of the estimated model for stock returns over the whole sample in Example 5.4 by using a predictive failure test of the last two years of observations. The following models would be estimated 1981M1–1992M12 (whole sample)
(5.74)
1981M1–1990M12 (‘long sub-sample’)
(5.75)
Can this regression adequately ‘forecast’ the values for the last two years? The test statistic would be given by (5.76)
Compare the test statistic with an F(24, 118) = 1.66 at the 5% level. So the null hypothesis that the model can adequately predict the last few observations would not be rejected. It would thus be concluded that the model did not suffer from predictive failure during the 1991M1–
1992M12 period.