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

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  • John B. Donaldson
  • Rajnish Mehra

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.

Suggested Citation

  • John B. Donaldson & Rajnish Mehra, 2021. "Average crossing time: An alternative characterization of mean aversion and reversion," Quantitative Economics, Econometric Society, vol. 12(3), pages 903-944, July.
    • Handle: RePEc:wly:quante:v:12:y:2021:i:3:p:903-944
    DOI: 10.3982/QE1560
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    More about this item

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
    • E3 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles
    • E44 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Financial Markets and the Macroeconomy
    • E47 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Forecasting and Simulation: Models and Applications
    • G1 - Financial Economics - - General Financial Markets
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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