Trouble with Rescaled Range algorithm

Serge Gonchar

2021 12 10

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5 次查看（30 天）

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Hello, everyone.

I'm trying to implement Rescaled Range algorithm from https://en.wikipedia.org/wiki/Rescaled_range and other sources, and using this generator https://uk.mathworks.com/matlabcentral/fileexchange/38935-fractional-brownian-motion-generator?s_tid=srchtitle to check how correct algorithm works. The problem is my algorithm doesn't work properly, Hurst estimation in the result is about source Hurst+0.5-0.9.

E.g. I set Hurst in fBm model = 0.1, alrogithm result is 0.59+. I tried to use several variations of code and still have same error

about Hurst+0.5-0.9. I ask you for help. Thank you a lot.

Here's the code of algorithm.

function [X,M,cumdev,rs,logRS,logN,H] = rsnew(x)
%UNTITLED2 Summary of this function goes here
%   Detailed explanation goes here
idx = size(x,1)-1;
n = idx;
rows = floor(idx/n);
c = 0;
while rows <= idx/2
    X = reshape(x(1:rows*n),rows,n); % если вернусь к N, заменить x на N
    M = ones(rows,n).*mean(X,2);
    demeaned = X - M;
    cumdev = cumsum(demeaned,2);
    rangeres = zeros(rows,n);
    for i = 1:rows
        for j = 1:n
            rangeres(i,j) = max(cumdev(i,1:j)) - min(cumdev(i,1:j));
        end
    end
    stdev = ones(rows,n).*std(X,1,2);
    rs = rangeres./stdev;
    
    averageRS(1,c+1) = mean(mean(rs,2)); 
    logRS(1,c+1) = log(averageRS(1,c+1));
    logN(1,c+1) = log(n);
    c = c+1;
    n = 2^(log2(n)-1); 
    rows = floor(idx/n);
end
H = logRS/logN;
p = polyfit(logN,logRS,9);
f = polyval(p,logN);
figure
plot(logN,logRS,'o')
hold on
plot(logN,f)
legend('logRS','f')
xlabel('log(number of test)'),ylabel('log(R/S)')
% axis([logN(1) logN(end) -inf +inf]),drawnow
end