TradingCalcHurst Exponent Calculator
RISK/STATS · HURST EXPONENT · ADVANCED
Rescaled-range (R/S) Hurst exponent: is a return series trending/persistent (H>0.5), mean-reverting (H<0.5), or consistent with a random walk (H~0.5)?
Comma, space, or newline separated. No thousand separators (write 43250.50, not 43,250.50).
Rescaled-range (R/S) analysis on a return series, not raw price levels. Needs enough data to produce at least 3 distinct window sizes at the chosen minimum window.
The formula
Classic rescaled-range (R/S) analysis:
- For each window size n: mean-center each chunk, take the cumulative sum, R = range of that cumulative series
- S = the chunk's own standard deviation
- H = the slope of log(mean R/S) vs. log(n), across every window size tested
Reading the result
- H > 0.5: trending / persistent (a move tends to be followed by a move the same way)
- H < 0.5: mean-reverting / anti-persistent (a move tends to reverse)
- H ≈ 0.5: consistent with a random walk, no exploitable memory
Where to go next
Hurst describes memory in a single series. To check whether two series share a long-run equilibrium relationship instead, see the cointegration test, or get the full risk/return picture with the portfolio tearsheet.
Use via API or MCP
This calculation is available as a deterministic API call for bots and AI agents.
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What assumptions and edge cases does this calculator use?
Give a return series, not price levels. It needs at least 32 values, and a minimum window that is a whole number of at least 4 (default 8); a series too short to give at least 3 window sizes is refused. R/S estimates are noisy on short samples, so a value near 0.5 is not a verdict. Not covered: confidence intervals, a short-sample bias correction and other estimators such as DFA.
What does the Hurst exponent measure?
Whether a time series has memory: does a move tend to be followed by a move in the same direction (trending/persistent, H>0.5), a move in the opposite direction (mean-reverting/anti-persistent, H<0.5), or is there no exploitable pattern at all (H~0.5, consistent with a random walk)?
How is it computed here?
Classic rescaled-range (R/S) analysis: the series is split into windows of several sizes, each window's cumulative-deviation range is divided by its standard deviation, and the Hurst exponent is the slope of log(mean R/S) regressed against log(window size).
Do I enter prices or returns?
Returns (or any already-stationary series), not raw price levels. Running R/S analysis on price levels directly would conflate an ordinary price trend with genuine long-range dependence in the increments: the same reasoning behind using returns (not levels) for correlation analysis.
How much data do I need?
At least 32 values, and enough beyond that to produce at least 3 distinct window sizes at your chosen minimum window (default 8). The window-halving process (32 -> 16 -> 8) needs enough total length to keep halving down to the minimum.
Is this a trading signal?
No. It's a descriptive statistic about a historical return series' memory structure, not a buy/sell recommendation. A high Hurst exponent describes past persistence; it doesn't guarantee it continues.