python 3線形回帰

目次
ガイドパック
データの取得
データパージ
第2のインポート方法
 infとnanのクリア
 訓練線形回帰方程式
そうごうそうかんパラメータ
クロスチェツク
異なる時期の相関
ガイドパック

import pandas as pd
import numpy as np
from urllib.request import urlretrieve

 データの取得

>>> vs_url = 'http://WWW.stoxx.com/download/historical_values/h_vstoxx.txt'
>>> es_url = 'http://WWW.stoxx.com/download/historical_values/hbrbcpe.txt'

urlretrieve(es_url ,  './data/es.txt')
('./data/es.txt', )
urlretrieve(vs_url ,  './data/vs.txt')
('./data/vs.txt', )

>>> lines = open('./data/es.txt', 'r').readlines()
>>> lines = [line.replace( ' ',"")for line in lines]
>>> lines[:6]
['PriceIndices-EUROCurrency
', 'Date;Blue-Chip;Blue-Chip;Broad;Broad;ExUK;ExEuroZone;Blue-Chip;Broad
', ';Europe;Euro-Zone;Europe;Euro-Zone;;;Nordic;Nordic
', ';SX5P;SX5E;SXXP;SXXE;SXXF;SXXA;DK5F;DKXF
', '31.12.1986;775.00;900.82;82.76;98.58;98.06;69.06;645.26;65.56
', '01.01.1987;775.00;900.82;82.76;98.58;98.06;69.06;645.26;65.56
']

データパージ

>>> new_file = open('./data/es50.txt', 'w')
>>> new_file.writelines('date' + lines[3][:-1]+ ';DEL' + lines[3][-1]) #   +：DEL+'
'
>>> new_file.writelines(line[4:])
>>> new_file.close()

 

>>> es = pd.read_csv ( './data/es50.txt' , index_col=0 ,parse_dates=True , sep=';' , dayfirst=True)
>>> np.round(es.tail())
              SX5P    SX5E   SXXP   SXXE   SXXF   SXXA    DK5F   DKXF  DEL
date                                                                      
2016-09-28  2847.0  2991.0  343.0  324.0  408.0  350.0  9072.0  581.0  NaN
2016-09-29  2849.0  2992.0  343.0  324.0  408.0  351.0  9112.0  583.0  NaN
2016-09-30  2843.0  3002.0  343.0  325.0  408.0  350.0  9116.0  583.0  NaN
2016-10-03  2845.0  2998.0  343.0  325.0  408.0  351.0  9131.0  584.0  NaN
2016-10-04  2871.0  3030.0  346.0  328.0  411.0  354.0  9212.0  589.0  NaN

>>>　del es['DEL']

第2のインポート方法

es2 = pd.read_csv(es_url, index_col=0 , parse_dates=True ,sep=';', dayfirst=True , header=None,skiprows=4 , names=cols)

es2.tail()
               SX5P     SX5E    SXXP    SXXE    SXXF    SXXA     DK5F    DKXF
2016-09-28  2846.55  2991.11  342.57  324.24  407.97  350.45  9072.09  581.27
2016-09-29  2848.93  2991.58  342.72  324.08  407.65  350.90  9112.09  582.60
2016-09-30  2843.17  3002.24  342.92  325.31  408.27  350.09  9115.81  583.26
2016-10-03  2845.43  2998.50  343.23  325.08  408.44  350.92  9131.24  584.32
2016-10-04  2871.06  3029.50  346.10  327.73  411.41  353.92  9212.05  588.71

vs = pd.read_csv ( './data/vs.txt' , index_col=0 ,parse_dates=True , sep=',' , header=2,dayfirst=True)

import datetime as dt
data = pd.DataFrame({'EUROSTOXX':es['SX5E'][es.index > dt.datetime(1999 ,1 ,1)]})
data = data.join(pd.DataFrame({'VSTOXX':vs['V2TX'][vs.index > dt.datetime(1999 ,1 ,1)]}))

>>> data = data.fillna(method='ffill')

data.plot(subplots=True,grid=True,figsize=(8,6))
array([,
       ],
      dtype=object)

rets = np.log(data/data.shift(1))

rets.head()
            EUROSTOXX    VSTOXX
date                           
1999-01-04        NaN       NaN
1999-01-05   0.017228  0.489248
1999-01-06   0.022138 -0.165317
1999-01-07  -0.015723  0.256337
1999-01-08  -0.003120  0.021570

>>> rets.plot(subplots=True,grid=True,figsize=(8,6))
array([,
       ],
      dtype=object)

 
 infとnanのクリア

import statsmodels.api as sm
rets[np.isnan(rets)] = 0
rets[np.isinf(rets)] = 0

 訓練線形回帰方程式

X = sm.add_constant(rets['EUROSTOXX'])
y = rets['VSTOXX']
result = sm.OLS(y,X).fit()

result.summary()

"""
                            OLS Regression Results                            
==============================================================================
Dep. Variable:                 VSTOXX   R-squared:                       0.526
Model:                            OLS   Adj. R-squared:                  0.525
Method:                 Least Squares   F-statistic:                     5042.
Date:                Thu, 14 Mar 2019   Prob (F-statistic):               0.00
Time:                        16:11:28   Log-Likelihood:                 8271.0
No. Observations:                4554   AIC:                        -1.654e+04
Df Residuals:                    4552   BIC:                        -1.653e+04
Df Model:                           1                                         
Covariance Type:            nonrobust                                         
==============================================================================
                 coef    std err          t      P>|t|      [0.025      0.975]
------------------------------------------------------------------------------
const       4.945e-05      0.001      0.085      0.932      -0.001       0.001
EUROSTOXX     -2.7539      0.039    -71.008      0.000      -2.830      -2.678
==============================================================================
Omnibus:                     1298.505   Durbin-Watson:                   2.084
Prob(Omnibus):                  0.000   Jarque-Bera (JB):            24719.917
Skew:                           0.875   Prob(JB):                         0.00
Kurtosis:                      14.279   Cond. No.                         66.5
==============================================================================

そうごうそうかんパラメータ

result.params
const        0.000049
EUROSTOXX   -2.753853
dtype: float64

import matplotlib.pyplot as plt 
plt.plot(rets['EUROSTOXX'],rets['VSTOXX'],'r.')
[]

ax  =  plt.axis() 
x = np.linspace(ax[0] ,ax[1] + 0.01)
plt.plot(rets['EUROSTOXX'],result.params.const+ result.params.EUROSTOXX*rets['EUROSTOXX'],'b',lw=2)
[]
plt.grid(True)
plt.axis('tight')
plt.xlabel('EURO  STOXX  50  returns')
plt.ylabel('VSTOXX  returns')

 クロスチェツク
 

rets.corr()
           EUROSTOXX    VSTOXX
EUROSTOXX   1.000000 -0.724945
VSTOXX     -0.724945  1.000000

 異なる時期の相関

>>> rets['EUROSTOXX'].rolling(window= 252).corr(rets['VSTOXX']).plot(grid=True , style='b')