Testing Mean Reversion with Stationarity, Hurst, and Half-Life Measures

Summary

This article introduces several ways to assess whether an exchange-rate series may suit a mean-reversion strategy. It explains the Augmented Dickey-Fuller test as a check for a unit root, the Hurst exponent as an indicator of trending or reverting behavior, and an estimated mean-reversion half-life derived from a regression of price changes on lagged prices. An AUD/NZD example reports an ADF statistic that does not cross the listed critical thresholds, alongside several Hurst estimates that mostly suggest trending behavior.

The article then describes a simple strategy that sizes long or short exposure according to the price’s distance from a moving average in standard-deviation units, using the estimated half-life to set the lookback. A moving-average slope filter is offered to suspend trading when the average moves too quickly. The material is an introductory illustration rather than evidence of a robust strategy: it sets transaction costs to zero in the example, gives limited testing detail, and notes that statistical indicators and parameter choices need further assessment.

Key ideas

• The Augmented Dickey-Fuller test assesses whether a series behaves as though it has a unit root.
• The Hurst exponent is presented as an indicator of trend persistence or mean-reverting behavior.
• A negative mean-reversion coefficient implies an estimated half-life, while a positive value suggests trend behavior.
• The example strategy scales exposure with the standardized distance from a moving average.
• A moving-average slope filter can close positions when the price trend becomes too strong.

Tags

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.