In [72]:

    

import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
import matplotlib as mpl
from arch import arch_model


    

In [75]:

    

mpl.rcParams["figure.figsize"] = [10, 5]


    

In [130]:

    

vix = pd.read_csv("data/vix.csv", usecols=(0,5), index_col=0, parse_dates=[0], na_values="null", dtype=np.float32)
vix = 100* vix.pct_change().dropna()


    

In [131]:

    

vix.plot()
plt.show()


    

In [132]:

    

am = arch_model(vix)


    

In [133]:

    

res = am.fit(update_freq=5)


    

    




Iteration:      5,   Func. Count:     37,   Neg. LLF: 13184.7316272495
Optimization terminated successfully.    (Exit mode 0)
            Current function value: 13184.420267396537
            Iterations: 9
            Function evaluations: 62
            Gradient evaluations: 9

In [134]:

    

res.summary()


    

    
Out[134]:





Constant Mean - GARCH Model Results

  
Dep. Variable:
      
Adj Close
     
  R-squared:         
  
  -0.000
 


  
Mean Model:
       
Constant Mean
   
  Adj. R-squared:    
  
  -0.000
 


  
Vol Model:
            
GARCH
       
  Log-Likelihood:    
 
  -13184.4


  
Distribution:
        
Normal
       
  AIC:               
 
   26376.8


  
Method:
        
Maximum Likelihood
 
  BIC:               
 
   26402.0


  
                        
          
  No. Observations:  
    
4004
   


  
Date:
           
Sat, Jul 22 2017
  
  Df Residuals:      
    
4000
   


  
Time:
               
22:07:24
      
  Df Model:          
      
4
    



Mean Model

   
     
coef
     
std err
      
t
       
P>|t|
     
95.0% Conf. Int.
  


  
mu
 
    0.1412
 
9.577e-02
 
    1.475
 
    0.140
 
[-4.647e-02,  0.329]



Volatility Model

      
        
coef
     
std err
      
t
       
P>|t|
    
95.0% Conf. Int.
  


  
omega
    
    4.1006
 
    1.377
 
    2.978
 
2.897e-03
  
[  1.402,  6.799]
 


  
alpha[1]
 
    0.1172
 
2.380e-02
 
    4.927
 
8.369e-07
 
[7.060e-02,  0.164]


  
beta[1]
  
    0.8000
 
4.225e-02
 
   18.936
 
5.769e-80
  
[  0.717,  0.883]
 

In [135]:

    

res.plot(annualize="D")
plt.show()


    

In [136]:

    

forecasts = res.forecast(horizon=5, method='simulation')


    

In [137]:

    

forecasts.variance.tail()


    

    
Out[137]:







  

    

      

      
h.1
      
h.2
      
h.3
      
h.4
      
h.5
    
    

      
Date
      

      

      

      

      

    
  
  

    

      
2017-05-10
      
NaN
      
NaN
      
NaN
      
NaN
      
NaN
    
    

      
2017-05-11
      
NaN
      
NaN
      
NaN
      
NaN
      
NaN
    
    

      
2017-05-12
      
NaN
      
NaN
      
NaN
      
NaN
      
NaN
    
    

      
2017-05-15
      
NaN
      
NaN
      
NaN
      
NaN
      
NaN
    
    

      
2017-05-16
      
28.038693
      
29.881232
      
31.288303
      
32.886916
      
34.296396
    
  

In [ ]: