Long-horizon regressions: theoretical results and applications

Abstract

I use asymptotic arguments to show that the t-statistics in long-horizon regressions do not converge to well-defined distributions. In some cases, moreover, the ordinary least squares estimator is not consistent and the R2 is an inadequate measure of the goodness of fit. These findings can partially explain the tendency of long-horizon regressions to find “significant” results where previous short-term approaches find none. I propose a rescaled t-statistic, whose asymptotic distribution is easy to simulate, and revisit some of the long-horizon evidence on return predictability and of the Fisher effect.