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] 💬

// C# usage syntax
IReadOnlyList<HurstResult> results =
  bars.ToHurst(lookbackPeriods);

Parameters

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

Historical price bars requirements

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

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

Response

IReadOnlyList<HurstResult>

• This method returns a time series of all available indicator values for the bars provided.
• It always returns the same number of elements as there are in the historical price bars.
• 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

property	type	description
Timestamp	DateTime	Date from evaluated TBar
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.

Utilities

• .Condense()
• .Find(lookupDate)
• .RemoveWarmupPeriods()
• .RemoveWarmupPeriods(removePeriods)

See Utilities and helpers for more information.

Chaining

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

// example
var results = bars
    .Use(CandlePart.HLC3)
    .ToHurst(..);

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

// example
var results = bars
    .ToHurst(..)
    .ToSlope(..);

See Chaining indicators for more.

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.

Streaming

Use the buffer-style List<T> when you need incremental calculations without a hub:

HurstList hurstList = new(lookbackPeriods);

foreach (IBar bar in bars)  // simulating stream
{
  hurstList.Add(bar);
}

// based on `ICollection<HurstResult>`
IReadOnlyList<HurstResult> results = hurstList;

Subscribe to a BarHub for advanced streaming scenarios:

BarHub barHub = new();
HurstHub observer = barHub.ToHurstHub(lookbackPeriods);

foreach (IBar bar in bars)  // simulating stream
{
  barHub.Add(bar);
}

IReadOnlyList<HurstResult> results = observer.Results;

See Buffer lists and Stream hubs for full usage guides.