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function H = hurst(x)
//Estimate the Hurst parameter of sample X via the rescaled range statistic.
//Calling Sequence:
//hurst(x)
//Parameters:
//x: x is a vector or matrix
//Description:
//This function estimates the Hurst parameter of sample x using the rescaled range statistic.
//If x is a matrix, the parameter is estimated for every column.
//Examples:
//hurst([10, 15, 3])
//ans = 0.045019
funcprot(0);
if (argn(2) ~= 1)
error("hurst: wrong number of input arguments");
end
if (isscalar(x))
error ("hurst: argument must not be a scalar");
end
if (isvector(x))
x = x(:);
end
[xr, xc] = size (x);
s = stdev(x, 'r');
y = [];
for i = 1:xr
y(i, :) = x(i, :) - mean(x, 'm');
end
w = cumsum(y);
RS = (max(w, 'r') - min(w, 'r')) ./ s;
H = log(RS) / log(xr);
endfunction
//input validation:
//assert_checkerror("hurst()", "hurst: wrong number of input arguments");
//assert_checkerror("hurst(1, 2, 3)", "Wrong number of input arguments.");
//assert_checkerror("hurst(1)", "hurst: argument must not be a scalar");
//tests:
//assert_checkalmostequal(hurst([1, 5, 7, 14, 6]), 0.31180, 5*10^-5);
//assert_checkalmostequal(hurst([3; 6; 9; 5]), 0.24271, 5*10^-5);
//assert_checkalmostequal(hurst([-1, 9, 4; 7, 4, -3; 6, 12, -18]),[ 0.124902, 0.063474, 0.084510], 5*10^-5);
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