Drawing Inferences from Statistics Based on Multiyear Asset Returns*

Researchers investigating the possibility of mean reversion in stock prices with statistics based on multiyear returns have noted difficulties in drawing inferences from these statistics because the approximating asymptotic distributions perform poorly. We develop an alternative asymptotic distribution theory for statistics involving multiyear returns. These distributions diPier markedly from those implied by the conventional theory. The 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.