Using R/S Analysis and the Hurst Exponent to Assess Market Persistence
Summary
This article presents rescaled range analysis as a way to estimate the Hurst exponent and characterize time-series behavior. It outlines the calculation: center observations around their mean, form cumulative deviations, measure their range, and scale that range by the series standard deviation. The exponent describes how this rescaled range changes as the observation window grows.
The article interprets values above 0.5 as persistence, values below 0.5 as anti-persistence, and values near 0.5 as consistent with a random walk. It also describes comparing observed R/S statistics with expected values under a random-walk null model, using a deviation threshold, and examining logarithmic V-statistics plots to infer cycles. Historical examples and a table of security and commodity estimates illustrate the approach, while a worked example combines cycle estimates across timeframes.
These estimates depend on the sample and timeframe. The author cautions that apparent cycles may be noise and recommends checking multiple timeframes and observation counts. The examples address a multiweek investment horizon and do not establish relevance for intraday trading.
Key ideas
- Rescaled range analysis relates the cumulative deviation range to the series standard deviation.
- A Hurst exponent above 0.5 is interpreted as persistence, while a value below 0.5 suggests anti-persistence.
- Values near 0.5 are treated as consistent with a random walk with limited serial dependence.
- Observed estimates can be compared with expected R/S values under a random-walk null model.
- Cycle estimates should be checked across timeframes because a single sample may reflect noise.
Tags
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.