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Hurst Exponent, Lyapunov exponent and the Stock market Predictability


This is the most concise article on the subject I know. Straight to the point. What are the instruments and how they can help you?

The article is about:

Hurst exponent

Lyapunov exponent

I had an em-mail correspondence with Mr. Dostal the author of the article. And I shared him that it looks like we need time series with large Hurst exponent. And within the series we look moments with low enough Lypaunov exponent. And on those series we can try to make forecasts with our machine learning algorythms.

His answer is that it looks mathematically correct. With the software found by Jaguar it is achievable.

The other software I know was only working under Linux and requires some knowledge to work with command line on Linux. Its authors hate GUI (not to mention the fact you need to compile by yourself and you need to install additional software in order to see the results). It was The Tisean software. The biggest problem was that I was not even sure I run the right commands and I had the right output. Well besides that Tisean is a great piece of Software.




  • JonnoB 2582 days ago

    Thanks for the link.

    One thing I found interesting was "When (Hi > Hi+1), the time series is persistent or trend reinforcing time series". I have always thought of H > 0.5 == persistent, H == 0.5 == random and H < 0.5 == anti persistent. It never crossed my mind to think about the rate of change.

  • jaguar1637 2582 days ago

    Well, JonnoB, John Last talked about this tip

    - Use iVAR to remove bad entries. In our standard expert advisor, we us a function named iVAR

    This function is : 

    bool iVAR()
    bool Result=false;
    double iVAR_1=iCustom(NULL,TimeFrame,"iVAR",5,1000,0,1);
    double iVAR_2=iCustom(NULL,TimeFrame,"iVAR",5,1000,0,2);
    if(iVAR_2<a3 && iVAR_1<a4)

    We have made several backtests and now, instead of using iVAR w/ the standard TimeFrame as M15, we use it w/ TimeFrame = M1

    also, we were working about the value of a3 and a4

    the value should be between 0.55 and 0.51 

    extern double a3 = 0.5x;
    extern double a4 = 0.5X;

    The goal is to remove bad entries and also Not to remove good entries

    The values of a3 & a4 may be  dependant of the selected broker, because I heared from another trader Luis, this value was varying