Journal of Applied Mathematics and Decision Sciences
Volume 2006 (2006), Article ID 12314, 21 pages
doi:10.1155/JAMDS/2006/12314
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.