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Hurst Exponent

ML Features statistics regime-detection hurst ml trending mean-reversion

Measures the persistence or anti-persistence of a time series using R/S analysis.

Visual Example

Hurst Exponent — annotated preview mapping to core implementation

Synthetic ideal per library logic. Generated 2026-06-25 IST via docs/generate_all_previews.py (reproducible; maps to core Next<T> implementation).

Description

The Hurst Exponent indicator is a technical analysis tool that measures the persistence or anti-persistence of a time series using r/s analysis.

This indicator is primarily used for identifying key market conditions. It provides a robust signal that can be easily integrated into both simple strategies and more complex machine learning feature pipelines. Compared to its alternatives, it offers a distinct balance of responsiveness and stability.

Traders often combine this with other metrics to confirm signals and avoid false positives during sideways market regimes. It remains a standard tool for systematic trading models.

Use to classify the current market regime. H > 0.5 suggests a trending market (persistent); H < 0.5 suggests a mean-reverting market (anti-persistent). Useful as a filter for trend-following or mean-reversion strategies.

The Hurst Exponent, pioneered by Harold Edwin Hurst in 1951, quantifies the 'memory' of a time series. In technical analysis, it distinguishes between trending, mean-reverting, and random walk price action. It is a critical feature for machine learning models to adapt their logic to the underlying market structure.

QuantWave implements this indicator via the universal Next<T> trait, guaranteeing bit-identical results between Rust streaming, Python streaming, and Polars batch (.ta() / map_batches) surfaces.

Formula / Specification

Implementation (quantwave-core/src/indicators/hurst.rs):

\[ H = \frac{\ln(R/S)}{\ln(N)} \]

Gold-standard parity vectors: quantwave-core/tests/gold_standard/hurst_exponent.json.

Parameters

Parameter Default Description
period 100 Lookback period for R/S analysis

Usage Examples

Streaming (Rust)

use quantwave_core::indicators::HURST_EXPONENT;
use quantwave_core::traits::Next;

let mut ind = HURST_EXPONENT::new(100);
for price in &prices {
    let value = ind.next(price);
}

Streaming (Python)

from quantwave import HURST_EXPONENT

ind = HURST_EXPONENT(100)
for price in prices:
    value = ind.next(price)

Polars Batch (Python)

import polars as pl
import quantwave as qw

def apply_hurst_exponent(series: pl.Series) -> pl.Series:
    ind = qw.HURST_EXPONENT(100)
    return pl.Series([ind.next(float(v)) for v in series.to_list()])

df = (
    pl.read_csv('ohlcv.csv')
    .lazy()
    .with_columns(
        pl.col("close").map_batches(apply_hurst_exponent, return_dtype=pl.Float64).alias("hurst_exponent")
    )
    .collect()
)

All surfaces are bit-identical via the single Next<T> implementation and proptests.

Edge Cases & Limitations

  • Warm-up: first 100 bars may return NaN or partial state per implementation.
  • Parameter sensitivity: smaller periods increase noise; larger periods increase lag.
  • Sudden gaps or bad ticks can distort rolling windows — consider pre-filtering.
  • Single-series indicators ignore volume unless otherwise documented.
  • Validated via proptests against gold-standard vectors where available.
  • No look-ahead bias; streaming and Polars batch paths are bit-identical.

Boundary Behavior

Condition Behavior
Warm-up Leading bars return NaN until warmup_bars is satisfied.
period > len When period exceeds series length, output is all NaN.
NaN inputs NaN in input propagates to output (NaN out).
Invalid params Non-positive period or missing required params raise ValueError.
Empty data Empty input returns an empty result series.

Sources & References

Primary Source: https://en.wikipedia.org/wiki/Hurst_exponent

Implementation: quantwave-core/src/indicators/hurst.rs (HURST_EXPONENT / HURST_EXPONENT_METADATA). Parity: quantwave-core/tests/gold_standard/hurst_exponent.json

Provenance: Standards bulk upgrade 2026-06-25 IST — see docs/DOCUMENTATION_STANDARDS.md.