In [1]:

    

import pandas as pd
import numpy as np
import matplotlib.pylab as plt
from statsmodels.tsa.seasonal import seasonal_decompose
from statsmodels.tsa.ar_model import AR
from sklearn.metrics import r2_score
%matplotlib inline
 
plt.rcParams['figure.figsize']=(20,10)
plt.style.use('ggplot')


    

In [2]:

    

sales_data = pd.read_csv('retail_sales.csv')
sales_data['date']=pd.to_datetime(sales_data['date'])
sales_data.set_index('date', inplace=True)


    

In [3]:

    

sales_data.head()


    

    
Out[3]:







  

    

      

      
sales
    
    

      
date
      

    
  
  

    

      
2009-10-01
      
338630
    
    

      
2009-11-01
      
339386
    
    

      
2009-12-01
      
400264
    
    

      
2010-01-01
      
314640
    
    

      
2010-02-01
      
311022
    
  

In [4]:

    

sales_data.plot()


    

    
Out[4]:





<matplotlib.axes._subplots.AxesSubplot at 0x7f9aeb094c10>






    

In [5]:

    

decomposed = seasonal_decompose(sales_data['sales'], model='additive')
x =decomposed.plot() #See note below about this


    

In [6]:

    

sales_data['stationary']=sales_data['sales'].diff()


    

In [7]:

    

sales_data.head()


    

    
Out[7]:







  

    

      

      
sales
      
stationary
    
    

      
date
      

      

    
  
  

    

      
2009-10-01
      
338630
      
NaN
    
    

      
2009-11-01
      
339386
      
756.0
    
    

      
2009-12-01
      
400264
      
60878.0
    
    

      
2010-01-01
      
314640
      
-85624.0
    
    

      
2010-02-01
      
311022
      
-3618.0
    
  

In [8]:

    

sales_data['stationary'].plot()


    

    
Out[8]:





<matplotlib.axes._subplots.AxesSubplot at 0x7f9ae8bbdc50>






    

In [9]:

    

decomposed = seasonal_decompose(sales_data['stationary'].dropna(), model='additive')
x =decomposed.plot() #See note below about this


    

In [10]:

    

pd.tools.plotting.lag_plot(sales_data['sales'])


    

    




/vagrant/pythondata/env/lib/python2.7/site-packages/ipykernel_launcher.py:1: FutureWarning: 'pandas.tools.plotting.lag_plot' is deprecated, import 'pandas.plotting.lag_plot' instead.
  """Entry point for launching an IPython kernel.






    
Out[10]:





<matplotlib.axes._subplots.AxesSubplot at 0x7f9ae6ae6610>






    

In [11]:

    

pd.tools.plotting.autocorrelation_plot(sales_data['sales'])


    

    




/vagrant/pythondata/env/lib/python2.7/site-packages/ipykernel_launcher.py:2: FutureWarning: 'pandas.tools.plotting.autocorrelation_plot' is deprecated, import 'pandas.plotting.autocorrelation_plot' instead.
  






    
Out[11]:





<matplotlib.axes._subplots.AxesSubplot at 0x7f9ae692f3d0>






    

In [12]:

    

sales_data['sales'].corr(sales_data['sales'].shift(12))


    

    
Out[12]:





0.97909859758957896

In [13]:

    

#create train/test datasets
X = sales_data['stationary'].dropna()

train_data = X[1:len(X)-12]
test_data = X[X[len(X)-12:]]


    

In [14]:

    

#train the autoregression model
model = AR(train_data)
model_fitted = model.fit()


    

    




/vagrant/pythondata/env/local/lib/python2.7/site-packages/statsmodels/tsa/base/tsa_model.py:171: ValueWarning: No frequency information was provided, so inferred frequency MS will be used.
  % freq, ValueWarning)

In [15]:

    

print('The lag value chose is: %s' % model_fitted.k_ar)


    

    




The lag value chose is: 10

In [16]:

    

print('The coefficients of the model are:\n %s' % model_fitted.params)


    

    




The coefficients of the model are:
 const             7720.952626
L1.stationary       -1.297636
L2.stationary       -1.574980
L3.stationary       -1.403045
L4.stationary       -1.123204
L5.stationary       -0.472200
L6.stationary       -0.014586
L7.stationary        0.564099
L8.stationary        0.792080
L9.stationary        0.843242
L10.stationary       0.395546
dtype: float64

In [17]:

    

# make predictions 
predictions = model_fitted.predict(
    start=len(train_data), 
    end=len(train_data) + len(test_data)-1, 
    dynamic=False)

# create a comparison dataframe
compare_df = pd.concat(
    [sales_data['stationary'].tail(12),
    predictions], axis=1).rename(
    columns={'stationary': 'actual', 0:'predicted'})


    

In [18]:

    

compare_df


    

    
Out[18]:







  

    

      

      
actual
      
predicted
    
    

      
date
      

      

    
  
  

    

      
2014-10-01
      
16831.0
      
5601.811846
    
    

      
2014-11-01
      
208.0
      
38414.120561
    
    

      
2014-12-01
      
63322.0
      
35441.708285
    
    

      
2015-01-01
      
-103980.0
      
-49947.389001
    
    

      
2015-02-01
      
-10317.0
      
-21617.841678
    
    

      
2015-03-01
      
57175.0
      
20818.987209
    
    

      
2015-04-01
      
-5893.0
      
14274.367772
    
    

      
2015-05-01
      
24398.0
      
15474.495929
    
    

      
2015-06-01
      
-14386.0
      
-12799.912704
    
    

      
2015-07-01
      
9481.0
      
10743.906740
    
    

      
2015-08-01
      
-1370.0
      
1184.598793
    
    

      
2015-09-01
      
-25423.0
      
-23880.339021
    
  

In [19]:

    

compare_df.plot()


    

    
Out[19]:





<matplotlib.axes._subplots.AxesSubplot at 0x7f9ae69f7610>






    

In [20]:

    

r2 = r2_score(sales_data['stationary'].tail(12), predictions)


    

In [21]:

    

r2


    

    
Out[21]:





0.63927217684780879

In [ ]: