Department of Economics
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.
Journal of Applied Mathematics and Decision Sciences
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mean reversion, variance ratio test, random walk, stock price, stock return
Lam, Kin, Chun Mei Wong, and Wing Keung Wong. "New variance ratio tests to identify random walk from the general mean reversion model." Journal of Applied Mathematics and Decision Sciences 2006 (2006): 1-21.