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Hurst Exponent

The Hurst Exponent (H) is part of a Rescaled Range Analysis, a random-walk path analysis that measures trending and mean-reverting tendencies of incremental return values. When H is greater than 0.5 it depicts trending. When H is less than 0.5 it is is more likely to revert to the mean. When H is around 0.5 it represents a random walk. [Discuss] 💬

chart for Hurst Exponent

// C# usage syntax
IEnumerable<HurstResult> results =
  quotes.GetHurst(lookbackPeriods);

Parameters

lookbackPeriods int - Number of periods (N) in the Hurst Analysis. Must be at least 20. Default is 100.

Historical quotes requirements

You must have at least N+1 periods of quotes to cover the warmup periods.

quotes is a collection of generic TQuote historical price quotes. It should have a consistent frequency (day, hour, minute, etc). See the Guide for more information.

Response

IEnumerable<HurstResult>

This method returns a time series of all available indicator values for the quotes provided.
It always returns the same number of elements as there are in the historical quotes.
It does not return a single incremental indicator value.
The first N periods will have null values since there’s not enough data to calculate.

HurstResult

Date DateTime - Date from evaluated TQuote

HurstExponent double - Hurst Exponent (H) from raw rescaled range (R/S) analysis

HurstExponentAL double - Anis-Lloyd corrected Hurst Exponent (H). Removes finite-sample bias from the raw R/S estimate. Like HurstExponent, values near 0.5 represent a random walk, greater than 0.5 depict trending, and less than 0.5 indicate mean-reverting behavior. This corrected value is generally preferred for smaller lookback periods.

Utilities

See Utilities and helpers for more information.

Chaining

This indicator may be generated from any chain-enabled indicator or method.

// example
var results = quotes
    .Use(CandlePart.HLC3)
    .GetHurst(..);

Results can be further processed on HurstExponent with additional chain-enabled indicators.

// example
var results = quotes
    .GetHurst(..)
    .GetSlope(..);

References

Inputs are log returns ln(c_t / c_{t-1}), which provide additive, scale-consistent increments.
HurstExponent (raw H) is the slope of log(R/S) against log(n) across chunk sizes, following the rescaled-range analysis of Hurst (1951) and Mandelbrot & Wallis (1969).
HurstExponentAL applies the Anis & Lloyd (1976) finite-sample expectation E[R/S]_n = Γ((n-1)/2) / (√π · Γ(n/2)) · Σ_{r=1}^{n-1} √((n-r)/r), then corrects each observed R/S as R/S − E[R/S]_n + √(π·n/2) before regressing. The expected value uses an exact LogGamma evaluation for n ≤ 340 and Peters’ (1994) Stirling approximation √(2 / (π·(n-1))) for larger n.