Data

In [25]:

    

%pylab inline


    

    




Populating the interactive namespace from numpy and matplotlib

In [26]:

    

# Import libraries
from __future__ import absolute_import, division, print_function

# Ignore warnings
import warnings
warnings.filterwarnings('ignore')


import numpy as np
import pandas as pd
import math

# Graphing Libraries
import matplotlib.pyplot as pyplt
from matplotlib.pylab import rcParams
rcParams['figure.figsize'] = 15, 6

import seaborn as sns
sns.set_style("white") 


from IPython.display import display


    

In [3]:

    

data = pd.read_csv('data/AirPassengers.csv', 
            parse_dates=[0], 
            index_col='Month')

data.head()


    

    
Out[3]:






  

    

      

      
#Passengers
    
    

      
Month
      

    
  
  

    

      
1949-01-01
      
112
    
    

      
1949-02-01
      
118
    
    

      
1949-03-01
      
132
    
    

      
1949-04-01
      
129
    
    

      
1949-05-01
      
121
    
  

In [4]:

    

ts = data['#Passengers'] 
ts.head(10)


    

    
Out[4]:





Month
1949-01-01    112
1949-02-01    118
1949-03-01    132
1949-04-01    129
1949-05-01    121
1949-06-01    135
1949-07-01    148
1949-08-01    148
1949-09-01    136
1949-10-01    119
Name: #Passengers, dtype: int64

In [5]:

    

ts['1949-01-01':'1949-05-01']


    

    
Out[5]:





Month
1949-01-01    112
1949-02-01    118
1949-03-01    132
1949-04-01    129
1949-05-01    121
Name: #Passengers, dtype: int64

In [6]:

    

pyplt.plot(ts);


    

In [7]:

    

from statsmodels.tsa.stattools import adfuller

def test_stationarity(timeseries):
    """
    Generate rolling statistic plot 
    
    Attributes
    ----------
    timeseries: pandas series
    """
    
    #Determing rolling statistics
    rolmean = pd.rolling_mean(timeseries, window=12)
    rolstd = pd.rolling_std(timeseries, window=12)

    #Plot rolling statistics:
    orig = plt.plot(timeseries, color='blue',label='Original')
    mean = plt.plot(rolmean, color='red', label='Rolling Mean')
    std = plt.plot(rolstd, color='black', label = 'Rolling Std')
    pyplt.legend(loc='best')
    pyplt.title('Rolling Mean & Standard Deviation')
    pyplt.show(block=False)

def Dickey_Fuller(timeseries):
    """
    Perform Dickey Fuller test for stationarity on the a timeseries
    
    Attributes
    ----------
    timeseries: pandas series
    """
    
    #Perform Dickey-Fuller test:
    print ('Results of Dickey-Fuller Test:')
    dftest = adfuller(timeseries, autolag='AIC')
    dfoutput = pd.Series(dftest[0:4], index=['Test Statistic','p-value','#Lags Used','Number of Observations Used'])
    for key,value in dftest[4].items():
        dfoutput['Critical Value (%s)'%key] = value
    print (dfoutput)


    

In [8]:

    

test_stationarity(ts)


    

In [9]:

    

Dickey_Fuller(ts)


    

    




Results of Dickey-Fuller Test:
Test Statistic                   0.815369
p-value                          0.991880
#Lags Used                      13.000000
Number of Observations Used    130.000000
Critical Value (5%)             -2.884042
Critical Value (1%)             -3.481682
Critical Value (10%)            -2.578770
dtype: float64

In [ ]: