├── README.md
├── LICENSE
└── Hurst.py


/README.md:
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 1 | # Hurst Exponent
 2 | Calculates the Hurst exponent of a time series based on Rescaled range (R/S) analysis.  
 3 | Reference: https://en.wikipedia.org/wiki/Hurst_exponent 
 4 | # Environment  
 5 | Python 3.6.2 AMD64  
 6 | numpy (1.13.3+mkl)  
 7 | pandas (0.20.3)  
 8 | # User Guide  
 9 | import Hurst  
10 | ts = list(range(50))  
11 | hurst = Hurst.hurst(ts)
12 | # Tips
13 | The input ts has to be object list(n_samples,) or np.array(n_samples,).
14 | 


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/LICENSE:
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 1 | MIT License
 2 | 
 3 | Copyright (c) 2018 RyanWangZf
 4 | 
 5 | Permission is hereby granted, free of charge, to any person obtaining a copy
 6 | of this software and associated documentation files (the "Software"), to deal
 7 | in the Software without restriction, including without limitation the rights
 8 | to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
 9 | copies of the Software, and to permit persons to whom the Software is
10 | furnished to do so, subject to the following conditions:
11 | 
12 | The above copyright notice and this permission notice shall be included in all
13 | copies or substantial portions of the Software.
14 | 
15 | THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
16 | IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
17 | FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
18 | AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
19 | LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
20 | OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
21 | SOFTWARE.
22 | 


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/Hurst.py:
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 1 | # -*- coding: utf-8 -*-
 2 | # Reference: https://en.wikipedia.org/wiki/Hurst_exponent
 3 | # python 3.6.2 AMD64
 4 | # 2018/4/19
 5 | # Calculate Hurst exponent based on Rescaled range (R/S) analysis
 6 | # How to use (example):
 7 | # import Hurst 
 8 | # ts = list(range(50))
 9 | # hurst = Hurst.hurst(ts)
10 | # Tip: ts has to be object list(n_samples,) or np.array(n_samples,)
11 | 
12 | __Author__ = "Ryan Wang"
13 | 
14 | import numpy as np
15 | import pandas as pd
16 | 
17 | def hurst(ts):
18 |     ts = list(ts)
19 |     N = len(ts)
20 |     if N < 20:
21 |         raise ValueError("Time series is too short! input series ought to have at least 20 samples!")
22 | 
23 |     max_k = int(np.floor(N/2))
24 |     R_S_dict = []
25 |     for k in range(10,max_k+1):
26 |         R,S = 0,0
27 |         # split ts into subsets
28 |         subset_list = [ts[i:i+k] for i in range(0,N,k)]
29 |         if np.mod(N,k)>0:
30 |             subset_list.pop()
31 |             #tail = subset_list.pop()
32 |             #subset_list[-1].extend(tail)
33 |         # calc mean of every subset
34 |         mean_list=[np.mean(x) for x in subset_list]
35 |         for i in range(len(subset_list)):
36 |             cumsum_list = pd.Series(subset_list[i]-mean_list[i]).cumsum()
37 |             R += max(cumsum_list)-min(cumsum_list)
38 |             S += np.std(subset_list[i])
39 |         R_S_dict.append({"R":R/len(subset_list),"S":S/len(subset_list),"n":k})
40 |     
41 |     log_R_S = []
42 |     log_n = []
43 |     print(R_S_dict)
44 |     for i in range(len(R_S_dict)):
45 |         R_S = (R_S_dict[i]["R"]+np.spacing(1)) / (R_S_dict[i]["S"]+np.spacing(1))
46 |         log_R_S.append(np.log(R_S))
47 |         log_n.append(np.log(R_S_dict[i]["n"]))
48 | 
49 |     Hurst_exponent = np.polyfit(log_n,log_R_S,1)[0]
50 |     return Hurst_exponent
51 |         
52 |         
53 | 
54 | 


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