% The Hurst exponent

%--------------------------------------------------------------------------

% The first 20 lines of code are a small test driver.

% You can delete or comment out this part when you are done validating the

% function to your satisfaction.

%

% Bill Davidson, quellen@yahoo.com

% 13 Nov 2005

function []=hurst_exponent()

disp('testing Hurst calculation');

n=100;

data=rand(1,n);

plot(data);

hurst=estimate_hurst_exponent(data);

[s,err]=sprintf('Hurst exponent = %.2f',hurst);disp(s);

%--------------------------------------------------------------------------

% This function does dispersional analysis on a data series, then does a

% Matlab polyfit to a log-log plot to estimate the Hurst exponent of the

% series.

%

% This algorithm is far faster than a full-blown implementation of Hurst's

% algorithm.  I got the idea from a 2000 PhD dissertation by Hendrik J

% Blok, and I make no guarantees whatsoever about the rigor of this approach

% or the accuracy of results.  Use it at your own risk.

%

% Bill Davidson

% 21 Oct 2003

function [hurst] = estimate_hurst_exponent(data0)   % data set

data=data0;         % make a local copy

[M,npoints]=size(data0);

yvals=zeros(1,npoints);

xvals=zeros(1,npoints);

data2=zeros(1,npoints);

index=0;

binsize=1;

while npoints>4

y=std(data);

index=index+1;

xvals(index)=binsize;

yvals(index)=binsize*y;

npoints=fix(npoints/2);

binsize=binsize*2;

for ipoints=1:npoints % average adjacent points in pairs

data2(ipoints)=(data(2*ipoints)+data((2*ipoints)-1))*0.5;

end

data=data2(1:npoints);

end % while

xvals=xvals(1:index);

yvals=yvals(1:index);

logx=log(xvals);

logy=log(yvals);

p2=polyfit(logx,logy,1);

hurst=p2(1); % Hurst exponent is the slope of the linear fit of log-log plot

return;

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