We make three contributions to using the variance ratio statistic at large horizons. Allowing for general heteroskedasticity in the data, we obtain the asymptotic distribution of the statistic when the horizon k is increasing with the sample size n but at a slower rate so that k/n 0. The test is shown to be consistent against a variety of relevant mean reverting alternatives when k/n 0. This is in contrast to the case when k/n > 0, where the statistic has been recently shown to be inconsistent against such alternatives. Second, we provide and justify a simple power transformation of the statistic that yields almost perfectly normally distributed statistics in finite samples, solving the well-known right skewness problem. Third, we provide a more powerful way of pooling information from different horizons to test for mean reverting alternatives. Monte Carlo simulations illustrate the theoretical improvements provided. 2006 Cambridge University Press.
