Assumptions for Hurst exponent calculation
The best is to calculate Hurst for stationary data (as then you can somehow find out if there are long range dependency signals which are not part of AR or MAs) but you can do non stationary as well. You can calculated froma fractal or wavelet transforms. Results are different   

In calculating Hurst you have to divide the data in short windows and average the results, (place a range the last 8 elements). Hurst can fluctuate significantly depending on the period you select.