When I look at the code for the compute_Hc function, 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.

The 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 the random_walk function correctly implemented? Because if it is correctly implemented, then the Wikipedia article needs to be corrected.

I have a cycle data, how I choose the "random_walk","change" and "price"? My data looks like Sin function.

Why do you require series length to be above 100 and not 50? Is this an arbitrary or universal condition? thttps://github.com/Mottl/hurst/blob/5ca5005485a679e6ce11a2769c948915ae27b2da/hurst/init.py#L146

Im new to Python, but I tried to run your code and it gets the message NameError: name 'hurst' is not defined....what can be done?

Hello, Sir,
I would like to question you about this part in "hurst":
"
elif kind == 'change':
incs = series
_series = np.hstack([[0.],np.cumsum(incs)])
mean_inc = (series[-1] - series[0]) / len(incs)
deviations = incs - mean_inc
Z = np.cumsum(deviations)
R = max(Z) - min(Z)
S = np.std(incs, ddof=1)
"
shouldn't it be there like this
"mean_inc = (_series[-1] - _series[0])/len(incs)"?
Sorry in advance if I am wrong.

I noticed that the compute_Hc result for some time series is less than 0 or greater than 1. Is this behavior intended?

MWE to reproduce this bug:

import hurst
import numpy as np

print("numpy", np.__version__)
print("hurst", hurst.__version__)
print()

np.random.seed(988)
H, _, _ = hurst.compute_Hc(np.random.uniform(size=100), kind="random_walk", simplified=True)
print(H) # -0.017687382184009826

np.random.seed(916)
H, _, _ = hurst.compute_Hc(np.random.uniform(size=100), kind="random_walk", simplified=False)
print(H) # -0.011722357538317393

np.random.seed(164)
H, _, _ = hurst.compute_Hc(np.random.exponential(1, size=100), kind="change", simplified=True)
print(H) # 1.0118591069505447

The error described in #4 still exists in the current release (0.0.4) and can give very different results.

Random series should return 0.5, but:

a=np.random.randint(100,size=(300))
H, c, data = compute_Hc(a)
print(sname,"H={:.4f}, c={:.4f}".format(H,c))

Hello! Just working with your code on a time series analysis, to compute the Hurst exponent of a equity, e.g. Google.

Here is the code:

import matplotlib.pyplot as plt
from hurst import compute_Hc
from datetime import datetime
import pandas_datareader as web

series = web.DataReader("GOOG", "yahoo", datetime(2000,1,1), datetime(2013,1,1))

H, c, data = compute_Hc(series['Adj Close'], kind='price', simplified=True)

Output: H 0.82083 C 0.5268

Following this resource for the Google stock a Hurst of 0.50788 was calculated -> https://www.quantstart.com/articles/basics-of-statistical-mean-reversion-testing

In your script c is the equivalent to the Hurst Exponent being calculated in above link? Or are the two methods not comparable?

Hi Dmitry,

I was working with the latest release of your Hurst Exponent implementation (https://pypi.org/project/hurst/) and am seeing a bit of strangeness. Specifically my crypto price series seems to be getting HE values > 1.0, which obviously is incorrect.

I did email you the notebook as I am unable to attach it here.

Thanks in advance for any help.