The variance ratio test with stable Paretian errors

This paper examines the distribution of the overlapping variance ratio (OVR) statistic when the errors are distributed with thick tails as described by the family of stable Paretian distributions. The asymptotic distribution of the OVR statistic, which depends on the characteristic exponent, can be estimated using simulation. It is found that the convergence of the distribution of the OVR statistic to its asymptotic limit is extremely slow. Thus, the asymptotic results will not be able to provide any useful approximation in finite samples. To facilitate the OVR statistic as a test for the random walk hypothesis, the tail quantiles are estimated for several finite sample sizes.