# Why does the Hurst package apply a finite-differencing step before doing rescaled range calculations?

When I look at the code for the compute_Hc function in the Hurst package for Python, there is an initial finite differencing step. Everything else after that agrees with Wikipedia's description of the Hurst exponent except it works with the derivative of the series, instead of the original series.

Their random_walk function, which is supposed to use Fractional Brownian Motion, seems to be in agreement with their compute_Hc function. If you remove the differencing step, then there ends up being disagreement. But then is their random_walk function correctly implemented? Because if it is correctly implemented, then the Wikipedia article needs to be corrected.

• The authors of the linked paper write: " data having fBm statistics will have a constant scaling exponent [i.e., Hurst exponent $H$] generally with a value close to 1. Only the scaling region constituted by data having fGn statistics will have a scaling exponent \$H<1." – corey979 Feb 8 at 12:23