# Hurst Exponent (Simple) [pig]

The Hurst exponent is used as a measure of long-term memory of time series. It relates to the autocorrelations of the time series and the rate at which these decrease as the lag between pairs of values increases.

The Hurst exponent is referred to as the "index of dependence" or "index of long-range dependence". It quantifies the relative tendency of a time series either to regress strongly to the mean or to cluster in a direction. A value H in the range 0.5–1 indicates a time series with long-term positive autocorrelation, meaning both that a high value in the series will probably be followed by another high value and that the values a long time into the future will also tend to be high. A value in the range 0 – 0.5 indicates a time series with long-term switching between high and low values in adjacent pairs, meaning that a single high value will probably be followed by a low value and that the value after that will tend to be high, with this tendency to switch between high and low values lasting a long time into the future. A value of H=0.5 can indicate a completely uncorrelated series, but in fact it is the value applicable to series for which the autocorrelations at small time lags can be positive or negative but where the absolute values of the autocorrelations decay exponentially quickly to zero. This in contrast to the typically power law decay for the 0.5 < H < 1 and 0 < H < 0.5 cases.

In plain words, when HE > 0.5, the market is trending and the volatility is high. When HE < 0.5, the market is mean reverting, and the volatility is low.
Hurst Exponent can be used to identify the strength of the trend in the market just like some traditional indicators such as ADX .

(This is not very accurate. The real HE test has an expected value that is close to 0.5 but not equal to 0.5. And we need to compute a confidence interval around the expected value of hurst exponent based on standard deviation. Eg : Expected Value 0.54, SD = 0. 05 , 95% confidence interval is 0.54 + 1.96* 0. 05 = 0.64, 0.54 - 1.96* 0. 05 = 0.44. So only when the HE value is larger than 0.64 or smaller than 0.44 it has statistical significance. Not just above 0.5 or below 0.5. ) We use 0.5 as threshold just for simplification, it's not the ideal way to do it. We see a lot of other Hurst Exponent Indicators using 0.5 as threshold but failed to mention this.

The estimation method here to calculate Hurst exponent is simplified. Therefore it does not provide the most accurate value. There are more advanced ways such as rescaled range and detrended fluctuation analysis to estimate the accurate values of Hurst exponent . However, these methods require a very large sample size such as 1024 bars, it makes it less tradable. It will be more like a statistical test for market efficiency rather than a trading indicator. We will release the rescaled range Hurst exponent estimation for accurate Hurst exponent in the future.
Release Notes: One mistake in the first picture. When market is trending the Hurst exponent should be > 0.5 instead of < 0.5

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