In [3]:

    

%matplotlib inline
import matplotlib.pyplot as plt
import statsmodels.api as sm
import pandas_datareader.data as pdr
import numpy as np
end='2016/9/30'
lnn225 = np.log(pdr.DataReader('NIKKEI225', 'fred', '1949/5/16', end)).dropna()
print(sm.tsa.adfuller(lnn225.NIKKEI225, regression='nc')[0])
print(sm.tsa.adfuller(lnn225.NIKKEI225, regression='nc')[1])
print(sm.tsa.adfuller(lnn225.NIKKEI225, regression='nc')[2])
print(sm.tsa.adfuller(lnn225.NIKKEI225, regression='nc')[3])
print(sm.tsa.adfuller(lnn225.NIKKEI225, regression='nc')[4])


    

    




2.17369686757
0.994169731135
38
16730
{'1%': -2.5658736531258919, '5%': -1.9410160670068219, '10%': -1.6168041340187047}

In [5]:

    

z = lnn225
y = z.diff().dropna()
x = z.shift(1).dropna()
model = sm.OLS(y,x)
results = model.fit()
print('without drift ', results.params[0])
x = sm.add_constant(x)
model = sm.OLS(y, x)
results = model.fit()
print('with drift ', results.params[0], results.params[1])
x['t'] = range(len(y))
model = sm.OLS(y, x)
results = model.fit()
print('with drift + time trend ', results.params[0], results.params[1], results.params[2])


    

    




without drift  2.64035301275e-05
with drift  0.00159089854801 -0.000156562803399
with drift + time trend  0.00155046216659 -0.000149176839762 -2.60661370915e-09

In [9]:

    

results.summary()


    

    
Out[9]:





OLS Regression Results

  
Dep. Variable:
        
NIKKEI225
    
  R-squared:         
  
   0.000
 


  
Model:
                   
OLS
       
  Adj. R-squared:    
  
   0.000
 


  
Method:
             
Least Squares
  
  F-statistic:       
  
   2.962
 


  
Date:
             
Tue, 24 Oct 2017
 
  Prob (F-statistic):
   
0.0517
  


  
Time:
                 
21:40:35
     
  Log-Likelihood:    
  
  49854.
 


  
No. Observations:
      
 16768
      
  AIC:               
 
-9.970e+04


  
Df Residuals:
          
 16765
      
  BIC:               
 
-9.968e+04


  
Df Model:
              
     2
      
                     
      
 
    


  
Covariance Type:
      
nonrobust
    
                     
      
 
    




      
         
coef
     
std err
      
t
      
P>|t|
  
[0.025
    
0.975]
  


  
const
     
    0.0016
 
    0.001
 
    1.869
 
 0.062
 
-7.56e-05
 
    0.003


  
NIKKEI225
 
   -0.0001
 
    0.000
 
   -1.145
 
 0.252
 
   -0.000
 
    0.000


  
t
         
-2.607e-09
 
    4e-08
 
   -0.065
 
 0.948
 
 -8.1e-08
 
 7.57e-08




  
Omnibus:
       
3202.752
 
  Durbin-Watson:     
 
   1.956
 


  
Prob(Omnibus):
  
 0.000
  
  Jarque-Bera (JB):  
 
67165.592


  
Skew:
           
-0.347
  
  Prob(JB):          
 
    0.00
 


  
Kurtosis:
       
12.780
  
  Cond. No.          
 
8.50e+04
 

In [10]:

    

lnw5000 = np.log(pdr.DataReader('WILL5000INDFC', 'fred', '1949/5/16', end)).dropna()
lnw5000.columns=['Close']
plt.plot(lnw5000.Close, color='hotpink')
lnw5000['t']=range(len(lnw5000))
model=sm.OLS(lnw5000.Close,lnw5000.t)
results=model.fit()
results.fittedvalues.plot(label='prediction',style='--')
plt.ylabel('log(w5000 index)')


    

    
Out[10]:





<matplotlib.text.Text at 0x284363c0278>






    

In [11]:

    

results.resid.hist(bins=50, color='lightgreen')
plt.ylabel('frequency')
plt.xlabel('residual')


    

    
Out[11]:





<matplotlib.text.Text at 0x284358a3fd0>






    

In [ ]: