HurstExponent — Hurst Exponent

A rescaled-range estimate of persistence: above 0.5 the series trends, below 0.5 it mean-reverts, 0.5 is a random walk. The classic answer to “is this instrument worth trend- following at all”.

Signature

HurstExponent(period, on=<source>)

Argument	Type	Required	Notes
period	int Param or literal	Yes	Return window. Default 64, bounds 16–400.
on=	symbol, OHLCV field, or indicator	No	Source. Defaults to the trade symbol’s close.

Formula

The window of log returns is cut into non-overlapping chunks of n/8, n/4, n/2 and n returns (newest first). Each chunk’s rescaled range R/S — the range of its cumulative deviations from its mean over its standard deviation — is averaged per size, and H is the least-squares slope of log(R/S) against log(size):

$$ H = \frac{k\sum x_i y_i - \sum x_i \sum y_i}{k\sum x_i^2 - (\sum x_i)^2}, \quad x_i = \log s_i, \quad y_i = \log \overline{(R/S)}_{s_i} $$

Warmup

period + 1 bars; 0.5 (the random-walk value) until then.

Reading the value

hurst.value
hurst.value > 0.55

Example

class HurstRegime(Strategy):
    """Trend-follow only in a persistent regime."""
    trade = Symbol()
    sizing = FixedCapital()

    def execute(self):
        hurst = HurstExponent(64, on=self.trade)
        sma = SMA(50, on=self.trade)
        if hurst.value > 0.55 and self.trade.close > sma.value and self.trade.is_flat:
            self.buy(self.trade, reason=f"Hurst {hurst.value:.2f}")
        if hurst.value < 0.45 and self.trade.is_long:
            self.sell(self.trade, self.trade.position, reason="Regime turned mean-reverting")

Notes

• Harold Hurst (1951); the classic rescaled-range regression across four window sizes.
• Not clamped. The estimate is the slope, whatever it is: on short windows R/S is biased upward and a reading can leave [0, 1]. An earlier two-scale version clamped to [0, 1] and so sat at exactly 0.00 or 1.00 on about one daily bar in seven — a flat line that meant “the estimate broke down”, not “the market is maximally persistent”. Minimum period is 16, so the smallest chunk holds two returns.