python3线性回归
目录
导包
获得数据
数据清洗
第二种导入方法
清除inf和nan
训练线性回归方程
总体相关参数
交叉检验
不同时期相关性
导包
import pandas as pd
import numpy as np
from urllib.request import urlretrieve获得数据
>>> 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\n', 'Date;Blue-Chip;Blue-Chip;Broad;Broad;ExUK;ExEuroZone;Blue-Chip;Broad\n', ';Europe;Euro-Zone;Europe;Euro-Zone;;;Nordic;Nordic\n', ';SX5P;SX5E;SXXP;SXXE;SXXF;SXXA;DK5F;DKXF\n', '31.12.1986;775.00;900.82;82.76;98.58;98.06;69.06;645.26;65.56\n', '01.01.1987;775.00;900.82;82.76;98.58;98.06;69.06;645.26;65.56\n']
数据清洗
>>> new_file = open('./data/es50.txt', 'w')
>>> new_file.writelines('date' + lines[3][:-1]+ ';DEL' + lines[3][-1]) #列数据+：DEL+'\n'
>>> 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']第二种导入方法
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) 
清除inf和nan
import statsmodels.api as sm
rets[np.isnan(rets)] = 0
rets[np.isinf(rets)] = 0
训练线性回归方程
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
==============================================================================
总体相关参数
result.params
const 0.000049
EUROSTOXX -2.753853
dtype: float64import 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') 
交叉检验
rets.corr()
EUROSTOXX VSTOXX
EUROSTOXX 1.000000 -0.724945
VSTOXX -0.724945 1.000000不同时期相关性
>>> rets['EUROSTOXX'].rolling(window= 252).corr(rets['VSTOXX']).plot(grid=True , style='b')
