Author Description

In the past two decades, long-horizon regression has become a popular choice for testing mean reversion in stock prices. Due to an overlapping and multi-period return summation, a finite-sample analysis of sample long-horizon regression coefficients is complicated and largely unavailable in the literature. Empirical studies rely almost entirely on asymptotic tests that can have serious size distortions and be highly unreliable in finite samples. We fill the void by providing a finite-sample analysis of the long-horizon regression under the assumption that stock returns follow a multivariate elliptical distribution. First, we derive analytical expressions for the moments of the OLS estimator of long-horizon regression slope coefficient, and provide simple formulas that approximate the mean and variance extremely well. Second, we develop efficient numerical procedures to compute the exact distribution, allowing us to perform an exact test. In addition, we propose a simple and reliable approximate test assuming the coefficient estimate to follow a normal distribution. Third, we analyze the size and power of the exact test under various popular alternatives. Using the exact test, we find that the power of the long-horizon regression test is very sensitive to the choice of the return horizon. Finally, when applied to the empirical data, the exact test lends less support of mean reversion than asymptotic tests. Even such moderate evidence is mainly due to the pre-1941 data.