MATLAB program for calculating the urlst Index

% The Hirst 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
% Function to your satisfaction.
%
% Bill David son, quellen@yahoo.com
% 13 Nov 2005

Function [] = hurst_exponent ()
Disp ('testing hustash calculation ');

N = 100;
Data = rand (1, N );
Plot (data );

Hirst = estimate_hurst_exponent (data );

[S, err] = sprintf ('hirst exponent = %. 2f ', hust'); disp (s );

% --------------------------------------------------------------------------
% This function does dispermissionanalysis on a data series, then does
% MATLAB polyfit to a log-log plot to estimate the Hirst exponent of
% Series.
%
% This algorithm is far faster than a full-blown Implementation of hurlsh's
% Algorithm. I got the idea from a 2000 PhD dissertation by Henderson Rik 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 David son
% 21 (Oct 2003)

Function [Hirst] = 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 );
Urst = P2 (1); % urst exponent is the slope of the Linear Fit of log-log plot

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