NEW VARIANCE RATIO TESTS TO IDENTIFY RANDOM WALK FROM THE GENERAL MEAN REVERSION MODEL

We develop some properties on the autocorrelation of the k-period returns for the gen-eral mean reversion (GMR) process in which the stationary component is not restricted to the AR(1) process but takes the form of a general ARMA process. We then derive some properties of the GMR process and three new nonparametric tests comparing the relative variability of returns over different horizons to validate the GMR process as an alternative to random walk. We further examine the asymptotic properties of these tests which can then be applied to identify random walk models from the GMR pro-cesses. Copyright © 2006 Kin Lam et al. This is an open access article distributed under the Cre-ative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 1