matlab求hurst指数代码

以下是MATLAB中求Hurst指数的示例代码：

function [H,rsq] = hurst(x)
% Implements the Hurst exponent calculation
%
% INPUTS:
% x: matrix of time series data (must be of size 2^N x M)
%
% OUTPUTS:
% H: Hurst exponent, indicating the nature of the time series (0 < H < 1)
% rsq: coefficient of determination of the linear regression fit
%
% EXAMPLE USAGE:
% H = hurst(x)
%
% Originally written by Dr. John Morgan - University of Warwick
% Modified by Max Little - University of Cambridge to return rsq
% Updated by Sarthak Mittal - IIT Delhi to comply with MATLAB best practices

% For details on the Hurst exponent see:
% Hurst, Harold E. (1951), "Long-term storage: An experimental study", 
% The Journal of Chemical Physics 18 (6): 636-651

% Check if the input has a size of 2^N x M
if ~isvector(x) && (log2(size(x,1))/log2(2)) == fix(log2(size(x,1))/log2(2))
    
    % Calculate the range of window sizes to fit
    range = 2:fix(log2(size(x,1)))-2;
    
    % Initialize the arrays that hold the Log(R/S) and Log(2^k) values
    logratio = zeros(length(range),1);
    log2n    = zeros(length(range),1);
    
    % Loop through all the window sizes
    for i = range
        
        % Calculate the number of windows and window size
        n = 2^i;
        m = floor(length(x)/n);
        
        % Initialize the arrays that hold the ranges and standard deviations
        ranges = zeros(m,1);
        stds   = zeros(m,1);
        
        % Loop through all the windows
        for j = 1:m
            
            % Extract the values in the current window
            indices = (1:n) + (j-1)*n;
            window  = x(indices);
            
            % Calculate the average and subtract it from the values
            avg = mean(window);
            window = window - avg;
            
            % Calculate the cumulative sum of the values
            cumsums = cumsum(window);
            
            % Find the range and standard deviation of the cumulative sums
            ranges(j) = max(cumsums) - min(cumsums);
            stds(j)   = std(window);
            
        end
        
        % Calculate the linear regression fit of Log(R/S) vs Log(2^k)
        logratio(i) = log(mean(ranges ./ stds));
        log2n(i)    = log(n); 
        
    end
    
    % Perform a linear regression fit between the Log(R/S) and Log(2^k) values
    p = polyfit(log2n,logratio,1);
    
    % Extract the slope of the linear regression fit
    H = p(1);
    
    % Calculate the coefficient of determination (r-squared value)
    rsq = 1 - sum((logratio - (p(1)*log2n + p(2))).^2) / ((length(logratio)-1)*var(logratio));
    
else
    
    % Error message for incorrect input size
    error('Error in hurst.m: Input must have a size of 2^N x M.')
    
end

end

要使用该函数，请按照以下步骤进行操作：

1.创建一个包含时间序列数据的向量或矩阵。

2.调用"hurst"函数，并将时间序列数据作为输入变量。例如：

H = hurst(x)

其中，"x"是包含时间序列数据的向量或矩阵，并且"H"是函数返回的Hurst指数。