In [1]:

    

from __future__ import print_function
import os
import pandas as pd
%matplotlib inline
from matplotlib import pyplot as plt


    

In [5]:

    

#Read dataset into a pandas.DataFrame
beer_df = pd.read_csv('datasets/quarterly-beer-production-in-aus-March 1956-June 1994.csv')
beer_df.index = beer_df['Quarter']


    

In [6]:

    

#Display shape of the dataset
print('Shape of the dataframe:', beer_df.shape)


    

    




Shape of the dataframe: (155, 2)

In [7]:

    

#Show top 10 rows
beer_df.head(10)


    

    
Out[7]:







  

    

      

      
Quarter
      
Quarterly beer production in Australia: megalitres. March 1956 ? June 1994
    
    

      
Quarter
      

      

    
  
  

    

      
1956Q1
      
1956Q1
      
284.4
    
    

      
1956Q2
      
1956Q2
      
212.8
    
    

      
1956Q3
      
1956Q3
      
226.9
    
    

      
1956Q4
      
1956Q4
      
308.4
    
    

      
1957Q1
      
1957Q1
      
262.0
    
    

      
1957Q2
      
1957Q2
      
227.9
    
    

      
1957Q3
      
1957Q3
      
236.1
    
    

      
1957Q4
      
1957Q4
      
320.4
    
    

      
1958Q1
      
1958Q1
      
271.9
    
    

      
1958Q2
      
1958Q2
      
232.8
    
  

In [8]:

    

#Rename the 2nd column
beer_df.rename(columns={'Quarterly beer production in Australia: megalitres. March 1956 ? June 1994':
                        'Beer_Prod'
                       },
               inplace=True
              )


    

In [9]:

    

#Remove missing values
missing = (pd.isnull(beer_df['Quarter'])) | (pd.isnull(beer_df['Beer_Prod']))
print('Number of rows with at least one missing values:', missing.sum())
beer_df = beer_df.loc[~missing, :]
print('Shape after removing missing values:', beer_df.shape)


    

    




Number of rows with at least one missing values: 1
Shape after removing missing values: (154, 2)

In [10]:

    

#In order to remove seasonal patterns let us calculate 2X4 quarter moving average
MA4 = beer_df['Beer_Prod'].rolling(window=4).mean()
TwoXMA4 = MA4.rolling(window=2).mean()
TwoXMA4 = TwoXMA4.loc[~pd.isnull(TwoXMA4)]


    

In [14]:

    

#Let's plot the original time series and the seasonal moving averages
fig = plt.figure(figsize=(5.5, 5.5))
ax = fig.add_subplot(1,1,1)
beer_df['Beer_Prod'].plot(ax=ax, color='b', linestyle='-')
TwoXMA4.plot(ax=ax, color='r', linestyle='-')
plt.xticks(rotation=60)
ax.set_title('Quaterly Beer Production between in Australia and 2X4 quarter MA')
plt.savefig('plots/ch2/B07887_02_16.png', format='png', dpi=300)


    

In [15]:

    

#Let's compute the residuals after removing the trend
residuals = beer_df['Beer_Prod']-TwoXMA4
residuals = residuals.loc[~pd.isnull(residuals)]


    

In [17]:

    

#Let's plot the residuals
fig = plt.figure(figsize=(5.5, 5.5))
ax = fig.add_subplot(1,1,1)
residuals.plot(ax=ax, color='b', linestyle='-')
plt.xticks(rotation=60)
ax.set_title('Residuals in Quaterly Beer Production time series')
plt.savefig('plots/ch2/B07887_02_17.png', format='png', dpi=300)


    

In [12]:

    

from pandas.plotting import autocorrelation_plot


    

In [13]:

    

#Let's plot the autocorrelation function of the residuals
fig = plt.figure(figsize=(5.5, 5.5))
ax = fig.add_subplot(1,1,1)
autocorrelation_plot(residuals, ax=ax)
ax.set_title('ACF of Residuals in Quaterly Beer Production time series')
plt.savefig('plots/ch2/B07887_02_18.png', format='png', dpi=300)
autocorrelation_plot(residuals)


    

    
Out[13]:





<matplotlib.axes._subplots.AxesSubplot at 0x7566550>






    

In [14]:

    

#Let's compute quarterly differecing to remove quaterly seasonality
residuals_qtr_diff = residuals.diff(4)


    

In [15]:

    

#Remove null values
residuals_qtr_diff = residuals_qtr_diff.loc[~pd.isnull(residuals_qtr_diff)]


    

In [16]:

    

#Let's plot the autocorrelation function of the residuals
fig = plt.figure(figsize=(5.5, 5.5))
ax = fig.add_subplot(1,1,1)
autocorrelation_plot(residuals_qtr_diff, ax=ax)
ax.set_title('ACF of Quaterly Differenced Residuals')
plt.savefig('plots/ch2/B07887_02_19.png', format='png', dpi=300)