Journal of Applied Mathematics and Decision Sciences
Volume 2006 (2006), Article ID 12314, 21 pages

New variance ratio tests to identify random walk from the general mean reversion model

Kin Lam,1 May Chun Mei Wong,2 and Wing-Keung Wong3

1Department of Finance & Decision Sciences, Hong Kong Baptist University, Hong Kong
2Dental Public Health, The University of Hong Kong, Hong Kong
3Department of Economics, Faculty of Arts & Social Sciences, National University of Singapore, 1 Arts Link, 117570, Singapore

Received 13 June 2005; Revised 30 November 2005; Accepted 9 December 2005

Copyright © 2006 Kin Lam et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We develop some properties on the autocorrelation of the k-period returns for the general 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 processes.