Hurst指数的Matlab实现

% 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;