Transformed regression-based long-horizon predictability tests

Taking stock of long-horizon predictability tests: Are factor returns predictable?

“…However, when K ! 1 with the sample size in the above scenario, both the standard long-horizon OLS estimator in (19) and the associated t-statistic would diverge to +1 if A = 10 6 and to 1 if A = 10 6 , giving rise to a probability of Type I error increasing to 1 with n for a two-sided rejection region or to a probability of Type I error increasing to 1 with n when A = 10 6 and decreasing to 0 when A = 10 6 for a one-sided rejection region. This irregularity is a consequence of the inconsistency of the standard OLS estimator in (11): a test based on a consistent estimator would continue to reject values of A very close to the null hypothesis up to the point when departures from the null hypothesis reach the Pitman local alternative (de…ned by the consistency rate of the estimator on which the test statistic is based) with correct probability of Type I error.…”