Journal of Applied Mathematics and Decision Sciences
Volume 2006 (2006), Article ID 12314, 21 pages
doi:10.1155/JAMDS/2006/12314
New variance ratio tests to identify random walk from the general mean reversion model
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.
Abstract
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.