Trend or mean reversion test
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Hurst exponent calculator
Has this market trended, reverted or walked at random? The Hurst exponent of your closes, corrected for short samples.
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The closes
The exponent
Hurst exponent 0.41 after the small-sample correction: this market is within chance of a random walk, leaning a little to mean reverting, and with this many closes that lean could be luck.
- Raw exponent
- 0.53 from the slope of the rescaled range on the window size. Short samples push it above 0.5 even for a random walk, so the corrected 0.41 is the one to read.
- How to read it
- 0.5 is a random walk. Clearly above it, trends have tended to persist, which suits trend following; clearly below it, moves have tended to reverse, which suits fading stretches.
- Read it with care
- Measured on 199 returns; with this many the exponent can be off by about 0.1 by chance alone. Hundreds of closes give a steadier number, and a market can change character.
Each window size: how many runs fit, their average rescaled range, and what a random walk of that length shows.
| Window | Runs | R/S | Random |
|---|---|---|---|
| 8 | 24 | 2.51 | 2.46 |
| 16 | 12 | 3.86 | 3.91 |
| 32 | 6 | 5.33 | 5.97 |
| 64 | 3 | 7.65 | 8.90 |
Education only, not investment advice. The answer comes from the numbers you typed in, not from your account or the market. Simulated results are hypothetical and have limits: real trading has slippage, gaps, changing results and emotions. Trading leveraged products can lose money quickly, including all of it. Risk warning
Educational only, not financial advice; trading involves risk.
Memory in the price
Harold Hurst measured the Nile's floods and found that wet years clustered: the range of the water level grew faster with time than chance allows. The same rescaled range test on a market's returns gives its Hurst exponent: 0.5 for a random walk, above it when moves have tended to persist, below it when they have tended to reverse. Short samples make every market look a little trending, so this page also shows the exponent after the Anis-Lloyd-Peters correction, which compares each window with what a random walk of that length shows.
Test the same question another way with the trend or mean reversion test, measure how fast stretches close with the mean reversion half-life calculator, see whether the market trends now with the choppiness index, and size the trade with the position size calculator.
Not advice. Statistics on the closes you type; a test on past prices does not predict the next ones.
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Mean reversion half-life calculator
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Choppiness index calculator
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Baroq never holds your money and never trades for you. Educational only, not financial advice; trading involves risk.