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Long-Horizon Regressions when the Predictor is Slowly Varying
SSRN eLibrary, (2004)
DOI: 10.2139/ssrn.564741
Аннотация
Predictive stock return regressions have two distinctive characteristics: i) the predictor on the right-hand side is persistent and its variance is orders of magnitude smaller than the variance of returns; (ii) the left-hand side variable is a long-horizon return constructed from overlapping sums of short-horizon returns. We offer a new model for the predictor that parsimoniously captures and links its persistence and small variance. We then use two asymptotic approaches to analyze the properties of long-horizon regressions. The approaches differ in their treatment of the overlap. One of the asymptotics has previously been analyzed with other data generating processes, while the second one is novel. We find that under both asymptotics, least-squares estimators are not consistent, their t-statistics diverge, and the R is not an adequate goodness-of-fit measure. Interestingly, a re-scaled version of the t-statistic is consistent under both long-horizon approximations and is suitable for testing predictability in long-horizon regressions. A Monte Carlo analysis of the finite-sample properties of the re-scaled t-statistic reveals that both approximations are accurate even for small sample sizes. We apply these results to test for predictability in returns of real estate investment trusts (REITs) which have come into existence only since the early 1970s and for which a reliable predictability test is crucial given the small dataset.
