# -*- coding: utf-8 -*- # Reference: https://en.wikipedia.org/wiki/Hurst_exponent # python 3.6.2 AMD64 # 2018/4/19 # Calculate Hurst exponent based on Rescaled range (R/S) analysis # How to use (example): # import Hurst # ts = list(range(50)) # hurst = Hurst.hurst(ts) # Tip: ts has to be object list(n_samples,) or np.array(n_samples,) __Author__ = "Ryan Wang" import numpy as np import pandas as pd def hurst(ts): ts = list(ts) N = len(ts) if N < 20: raise ValueError("Time series is too short! input series ought to have at least 20 samples!") max_k = int(np.floor(N/2)) R_S_dict = [] for k in range(10,max_k+1): R,S = 0,0 # split ts into subsets subset_list = [ts[i:i+k] for i in range(0,N,k)] if np.mod(N,k)>0: subset_list.pop() #tail = subset_list.pop() #subset_list[-1].extend(tail) # calc mean of every subset mean_list=[np.mean(x) for x in subset_list] for i in range(len(subset_list)): cumsum_list = pd.Series(subset_list[i]-mean_list[i]).cumsum() R += max(cumsum_list)-min(cumsum_list) S += np.std(subset_list[i]) R_S_dict.append({"R":R/len(subset_list),"S":S/len(subset_list),"n":k}) log_R_S = [] log_n = [] print(R_S_dict) for i in range(len(R_S_dict)): R_S = (R_S_dict[i]["R"]+np.spacing(1)) / (R_S_dict[i]["S"]+np.spacing(1)) log_R_S.append(np.log(R_S)) log_n.append(np.log(R_S_dict[i]["n"])) Hurst_exponent = np.polyfit(log_n,log_R_S,1)[0] return Hurst_exponent