Average crossing time: An alternative characterization of mean aversion and reversion

Abstract

This study compares and contrasts the multiple characterizations of mean reversion in financial time series as regards the restrictions they imply. This is accomplished by translating them into statements about an alternative measure, the “Average Crossing Time” or ACT. We argue that the ACT measure, per se, provides not only a useful benchmark for the degree of mean reversion/aversion, but also an intuitive, and easily quantified sense of one time series being “more strongly mean‐reverting/averting” than another. We conclude our discussion by deriving the ACT measure for a wide class of stochastic processes and detailing its statistical characteristics. Our analysis is principally undertaken within a class of well‐understood production based asset pricing models.