[]=hurst_exponent()

% 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, [e-mail]
% 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;