Hurst Exponent Theory

The Hurst exponent  is applicable in several areas of applied mathematics such as  fractals and chaos theory. The Hurst  exponent can yield interesting results when applied to financial data. Finance data have a fractal nature,  has lead a lot of mathematician  to apply the mathematics of fractals and chaos analyzing financial time series.

A few references are listed below:

Benoit Mandelbrot, who later became famous for his work on fractals, wrote the early papers on the application of the Hurst exponent to financial time series. Many of these papers are collected in Mandelbrot's book Fractals and Scaling in Finance, Springer Verlag, 1997.


 
Edgar Peters' book Chaos and Order in the Capital markets, Second Edition spends two chapters discussing the Hurst exponent and its calculation using the the rescaled range (RS) technique. Unfortunately, Peters only applies Hurst exponent estimation to a few time series and provides little solid detail on the accuracy of Hurst exponent calculation for data sets of various sizes.



The Hurst exponent is used as a measure of the long term memory of time series, i.e. the autocorrelation of the time series. Where a value of 0 < H < 0.5 indicates a time series with negative autocorrelation (e.g. a decrease between values will probably be followed by an increase), and a value of 0.5 < H < 1 indicates a time series with positive autocorrelation (e.g. an increase between values will probably be followed by another increase). A value of H=0.5 indicates a true random walk, where it is equally likely that a decrease or an increase will follow from any particular value (e.g. the time series has no memory of previous values)

The Three Principles of Hurst Exponent

 Value 0.5 – 1 = whatever is happening now is likely to continue
 Value 0 – 0.5 = whatever is happening now is likely to reverse
 Value around 0.5 = likely to go in any direction

Trading Strategy Based on Hurst Exponent

Hurst Value around 0.5 = likely to go in any direction 
This situation  very very suitable for scalping strategies. Very low probability of breakdown  of the trading channel.


Value 0 – 0.5 = whatever is happening now is likely to reverse.
Best way to waiting for divergence signal (arrow)  and find reverse zone.

Value 0.5 – 1 = whatever is happening now is likely to continue
Keep current position.



Pic.1 - Indicator Hurst Divergence

Trading Signals (see Pic. 1)

Signal 1 - Hurst Exponent:  Value 0 – 0.5,   Divergence:  down arrow -   Sell signal
Signal 2 - Hurst Exponent: Value 0 – 0.5 Divergence: up arrow - Close Sell and Buy Signal
Signal 3 - Hurst Exponent: Value 0.5 – 1  Divergence: down arrow - Ignore

Read more about MetaTrader Indicator Hurst Divergence

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