Estimating the Hurst Exponent with Detrended Fluctuation Analysis
Summary
The document describes a ProBuilder implementation of detrended fluctuation analysis for estimating a Hurst exponent from log returns. It centers and cumulatively sums returns, divides the resulting series into blocks at multiple scales, removes a linear trend within each block, and measures the remaining fluctuation. A regression of log fluctuation against log scale provides the exponent estimate.
The indicator compares that estimate with a random-walk reference of 0.5 and displays confidence bounds around the reference, with colors distinguishing regions above and below those thresholds. It also outputs a smoothed estimate. These readings can help investigate persistence or anti-persistence in time series, but the document presents no empirical validation or trading rules. Its author warns that the repeated calculations are computationally intensive and unsuitable for real-time use, so it is best treated as an analytical experiment rather than a live signal.
Key ideas
- The method estimates scaling behavior by relating detrended fluctuation to block size across multiple scales.
- It applies the analysis to centered cumulative log returns.
- The Hurst estimate is interpreted relative to 0.5, with confidence bounds used to distinguish deviations from the random-walk reference.
- A smoothed version is displayed alongside the raw estimate and thresholds.
- The implementation is computationally demanding and is not recommended for real-time use.
Tags
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.