Drawing Inferences from Statistics Based on Multi-Year Asset Returns

Abstract

The possibility of mean reversion in stock prices recently has been examined using statistics based on multi-year returns. Previous researchers have noted difficulties in drawing inferences about these statistics because of poor performance of the usual approximating asymptotic distributions. We therefore develop an alternative asymptotic distribution theory for statistics involving multi-year returns. These distributions differ markedly from those implied by the conventional theory. This alternative theory provides substantially better approximations to the relevant finite-sample distributions. It also leads to empirical inferences much less at odds with the hypothesis of no mean reversion.