In [1]:

    

import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
%matplotlib inline


    

In [2]:

    

eurusd = pd.read_csv("data/EURUSD_daily.csv", index_col='Date')


    

In [3]:

    

eurusd.index = pd.to_datetime(eurusd.index)


    

In [4]:

    

eurusd = eurusd['2007-01-01':'2008-05-01']


    

In [5]:

    

eurusd.head()


    

    
Out[5]:







  

    

      

      
EUR/USD Close
    
    

      
Date
      

    
  
  

    

      
2007-01-01
      
1.3146
    
    

      
2007-01-02
      
1.3287
    
    

      
2007-01-03
      
1.3163
    
    

      
2007-01-04
      
1.3085
    
    

      
2007-01-05
      
1.3009
    
  

In [6]:

    

eurusd.describe().transpose()


    

    
Out[6]:







  

    

      

      
count
      
mean
      
std
      
min
      
25%
      
50%
      
75%
      
max
    
  
  

    

      
EUR/USD Close
      
349.0
      
1.408096
      
0.08286
      
1.289
      
1.3434
      
1.3797
      
1.4668
      
1.5997
    
  

In [7]:

    

eurusd.plot(figsize=(16,9))


    

    
Out[7]:





<matplotlib.axes._subplots.AxesSubplot at 0x7fb31cf22a90>






    

In [8]:

    

timeseries = eurusd['EUR/USD Close']


    

In [9]:

    

timeseries.rolling(12).mean()['2007-09-01':'2008-09-01'].plot(label='12 Month MA', figsize = (16,9))
#timeseries.rolling(12).std()['2007-09-01':'2008-09-01'].plot(label='12 Month rolling STD')
timeseries['2007-09-01':'2008-09-01'].plot()
plt.legend(loc='best')


    

    
Out[9]:





<matplotlib.legend.Legend at 0x7fb31aeaa518>






    

In [2]:

    

from statsmodels.tsa.stattools import adfuller


    

    




/usr/local/lib/python3.5/dist-packages/statsmodels/compat/pandas.py:56: FutureWarning: The pandas.core.datetools module is deprecated and will be removed in a future version. Please use the pandas.tseries module instead.
  from pandas.core import datetools

In [11]:

    

result = adfuller(timeseries)


    

In [12]:

    

def adf_test(time_series):
    """
    Pass in a time series, returns ADF report
    """
    result = adfuller(time_series)
    print('Augmented Dickey-Fuller Test:')
    labels = ['ADF Test Statistic','p-value','#Lags Used','Number of Observations Used']

    for value,label in zip(result,labels):
        print(label+' : '+str(value) )
    
    if result[1] <= 0.05:
        print("Data is stationary")
    else:
        print("Data is non-stationary ")


    

In [13]:

    

adf_test(timeseries)


    

    




Augmented Dickey-Fuller Test:
ADF Test Statistic : -0.256525508468
p-value : 0.931439917962
#Lags Used : 0
Number of Observations Used : 348
Data is non-stationary 

In [14]:

    

eurusd['Fx rate first difference'] = eurusd['EUR/USD Close'] - eurusd['EUR/USD Close'].shift(1)


    

In [15]:

    

adf_test(eurusd['Fx rate first difference'].dropna())


    

    




Augmented Dickey-Fuller Test:
ADF Test Statistic : -18.7277242622
p-value : 2.03142004844e-30
#Lags Used : 0
Number of Observations Used : 347
Data is stationary

In [16]:

    

eurusd['Fx rate first difference'].plot(figsize = (16,9))


    

    
Out[16]:





<matplotlib.axes._subplots.AxesSubplot at 0x7fb3117af550>






    

In [17]:

    

from statsmodels.graphics.tsaplots import plot_acf, plot_pacf


    

In [28]:

    

fig = plt.figure(figsize=(16,9))
ax = fig.add_axes([0,0,1,1])
first_diff_acf = plot_acf(eurusd['Fx rate first difference'].dropna(), ax=ax)
ax.set_xlim(-1,150)


    

    
Out[28]:





(-1, 150)






    

In [19]:

    

fig = plt.figure(figsize=(16,9))
ax = fig.add_axes([0,0,1,1])
first_diff_pacf = plot_pacf(eurusd['Fx rate first difference'].dropna(), lags=40, ax=ax)


    

In [20]:

    

from statsmodels.tsa.arima_model import ARIMA


    

In [21]:

    

model = ARIMA(timeseries,order=(5,1,0))


    

In [22]:

    

model_fit = model.fit()


    

In [23]:

    

print(model_fit.summary())


    

    




                             ARIMA Model Results                              
==============================================================================
Dep. Variable:        D.EUR/USD Close   No. Observations:                  348
Model:                 ARIMA(5, 1, 0)   Log Likelihood                1250.463
Method:                       css-mle   S.D. of innovations              0.007
Date:                Mon, 16 Oct 2017   AIC                          -2486.926
Time:                        19:11:31   BIC                          -2459.961
Sample:                    01-02-2007   HQIC                         -2476.191
                         - 05-01-2008                                         
=========================================================================================
                            coef    std err          z      P>|z|      [0.025      0.975]
-----------------------------------------------------------------------------------------
const                     0.0007      0.000      1.923      0.055   -1.27e-05       0.001
ar.L1.D.EUR/USD Close    -0.0091      0.054     -0.168      0.867      -0.116       0.097
ar.L2.D.EUR/USD Close     0.0511      0.055      0.935      0.351      -0.056       0.158
ar.L3.D.EUR/USD Close    -0.0725      0.055     -1.323      0.187      -0.180       0.035
ar.L4.D.EUR/USD Close     0.0141      0.055      0.257      0.798      -0.094       0.122
ar.L5.D.EUR/USD Close    -0.0106      0.055     -0.194      0.847      -0.118       0.097
                                    Roots                                    
=============================================================================
                 Real           Imaginary           Modulus         Frequency
-----------------------------------------------------------------------------
AR.1           -1.8252           -0.0000j            1.8252           -0.5000
AR.2            1.8420           -1.6505j            2.4733           -0.1163
AR.3            1.8420           +1.6505j            2.4733            0.1163
AR.4           -0.2672           -2.8883j            2.9006           -0.2647
AR.5           -0.2672           +2.8883j            2.9006            0.2647
-----------------------------------------------------------------------------

In [24]:

    

residuals = pd.DataFrame(model_fit.resid)
residuals.plot()


    

    
Out[24]:





<matplotlib.axes._subplots.AxesSubplot at 0x7fb30b4b98d0>






    

In [25]:

    

residuals.describe().transpose()


    

    
Out[25]:







  

    

      

      
count
      
mean
      
std
      
min
      
25%
      
50%
      
75%
      
max
    
  
  

    

      
0
      
348.0
      
-0.000001
      
0.006666
      
-0.021268
      
-0.003472
      
0.000023
      
0.0035
      
0.023518
    
  

In [ ]:

    




    

In [ ]:

    




    

In [26]:

    

#fig = plt.figure(figsize=(16,9))
#ax = fig.add_axes([0,0,1,1])
#irst_diff_acf = plot_acf(eurusd['Fx rate first difference'].dropna(), ax=ax)
#ax.set_xlim(-1,150)
#x.set_ylim(-.1,.1)


    

In [32]:

    

eurusd['forecast'] = model_fit.predict(start = '2008-04-04', end = '2008-05-04', dynamic=True, typ='levels')


    

In [37]:

    

figFor = plt.figure(figsize = (16,9))
ax = figFor.add_axes([0,0,1,1])
ax.plot(eurusd['EUR/USD Close'])
ax.plot(eurusd['forecast'])
ax.set_xlim('2008-04-04', '2008-05-04')
ax.set_ylim(1.5,1.65)


    

    
Out[37]:





(1.5, 1.65)






    

In [38]:

    

eurusd['forecast'].plot()


    

    
Out[38]:





<matplotlib.axes._subplots.AxesSubplot at 0x7fb3102872e8>






    

In [ ]: