Description

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 ( Wikipedia).

In trading, the Hurst exponent can hint whether the product is trending or ranging around the moving average:

1. Whenever the Hurst’s value is 0 <= H < 0.5, it might mean the product is ranging around the moving average.
2. Whenever the Hurst’s value is 0.5 < H <= 1, it might mean that the product is trending towards a specific direction, either long or short.
3. Whenever the Hurst’s value is 0.5, this value means that the product is either ranging nor trending.

Usage

1. Save the HurstExponent.ex4 under the Indicators folder.
2. Attach the HurstExponent.ex4 indicator to any product, select how many historical points you would like to calculate and see the result in the sub chart (the more historical points you calculate, the longer you would have to wait until the output chart is ready, must be >=1).

As seen in the attached images, I attached the Hurst exponent to two daily charts, USDJPY & GBPUSD:

For USDJPY, Hurst exponent value equals 0.2090 which is in the mean reverting range. We can see clearly that USDJPY daily price is fluctuating around the 200 days moving average without an obvious trend.

For GBPUSD on the other hand, Hurst exponent value equals 0.6031 which is in the trending range. We can see clearly that GBPUSD daily price has an upward trend above the 200 days moving average following a downward trend.

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