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.

中文翻译：

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平均穿越时间：均值厌恶和回归的另一种表征

本研究比较和对比了金融时间序列中均值回归的多重特征，以及它们所暗示的限制。这是通过将它们转换为关于替代措施“平均穿越时间”或 ACT 的陈述来实现的。我们认为 ACT 测量本身不仅为均值回归/厌恶程度提供了一个有用的基准，而且还提供了一种直观且易于量化的感觉，即一个时间序列比另一个“更强烈的均值回归/回避” . 我们通过推导广泛类别的随机过程的 ACT 度量并详细说明其统计特征来结束我们的讨论。我们的分析主要是在一类易于理解的基于生产的资产定价模型中进行的。