Drawing Inferences From Statistics Based on Multi-Year Asset Returns
James H. Stock
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.
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