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

摘要

We develop some properties on the autocorrelation ofthek-period returns for the general mean reversion (GMR)process in which the stationary component is not restricted to theAR(1) process but takes the form of a general ARMA process. Wethen derive some properties of the GMR process and three newnonparametric tests comparing the relative variability of returnsover different horizons to validate the GMR process as analternative to random walk. We further examine the asymptoticproperties of these tests which can then be applied to identifyrandom walk models from the GMR processes.