Title: The Power and Size of Mean Reversion Tests

Status: Forthcoming, Journal of Empirical Finance, 2001

Abstract:

I develop a method which allows analytical calculation of the power of tests of mean reversion. This method is used to calculate the optimal form of the weighted autocorrelation test, long-horizon regression, variance-ratio, weighted spectral tests, and any instrumental variable or generalized method of moment (GMM) tests which use linear functions of past returns as instruments. I demonstrate the asymptotic optimality of these tests. I develop a simple geometric intuition for these tests, and make power comparisons across tests of this class. I conduct Monte-Carlo experiments to investigate small sample robustness. Finally, I revisit the evidence on mean-reversion in stock prices based on these results, and find considerably more evidence in favor of a mean reversion hypothesis than found in other studies. I show that the difference is attributable to the low power of these other tests.

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