Time series analysis using python.


To analyse the furniture sales data in superstore sales data set in python.

  • Import necessary libraries.
  • Read the data set.
  • Take necessary columns from the data set.
  • Drop
  • all other columns.
  • Make data column as index.
  • Select the predictor variable as per the requirements.
  • Check the time series stationarity.
  • Check, is the time series having trend and seasonality.
  • Calculate rolling mean and rolling standard deviation.
  • If there is trend and seasonality in the time series, eliminate those things.
  • Take test statistics value and critical values using Dickey-Fuller test.
  • If test statistics value is greater than critical value then the time series is not stationarity.
  • Make again time series as stationarity until the statistics value is less than critical value.
  • Plot the time series.
  • Plot the rolling mean and rolling standard deviation.
  • Plot the residual,trend,observations and seasonality.
  • Find optimal number of parameters(p,d,q) using less AIC value combination.
  • Fit the ARIMA model.
  • Take the summary of the model.
  • Validate the model.
  • Do forecast for the model.

#import libraries

import warnings

import itertools

import numpy as np

import matplotlib.pyplot as plt

%matplotlib inline



import pandas as pd

import statsmodels.api as sm

import matplotlib

from statsmodels.tsa.stattools import adfuller

#Reading the data

data = pd.read_excel(“/home/soft23/soft23

furniture = data.loc[data[‘Category’] == ‘Furniture’]

#unwanted columns

cols = [‘Row ID’, ‘Order ID’, ‘Ship Date’, ‘Ship Mode’, ‘Customer ID’, ‘Customer Name’, ‘Segment’,

‘Country’, ‘City’, ‘State’, ‘Postal Code’, ‘Region’, ‘Product ID’, ‘Category’, ‘Sub-Category’,

‘Product Name’, ‘Quantity’, ‘Discount’, ‘Profit’]

furniture.drop(cols, axis=1, inplace=True)

furniture = furniture.sort_values(‘Order Date’)

df = pd.DataFrame(furniture)

df = furniture.set_index(‘Order Date’)

print(“Index of the data frame\n\n”,df.index)

ts = df[‘Sales’].resample(‘MS’).mean()


print(“Actual Time series is\n\n”,ts)


#total length of time series

print(“Length of time series in months:”,len(ts))


#First 5 rows of time series

print(“head of the time series:\n\n”,ts.head())


#check stationarity

print(“Sales of furniture over the years\n\n”)

ts.plot(figsize=(20,10), linewidth=3, fontsize=20)

plt.xlabel(‘Order Date’,fontsize=20)


print(“Rolling mean and standard deviation of time series\n\n”)

def test_stationarity(timeseries):

#Determing rolling statistics

rolmean = timeseries.rolling(window=12).mean()

rolstd = timeseries.rolling(window=12).std()

#Plot rolling statistics

timeseries.plot(figsize=(20,10), linewidth=3, fontsize=20)

plt.xlabel(‘Order Date’,fontsize=20)

rolmean.plot(figsize=(20,10), linewidth=3, fontsize=20)

plt.xlabel(‘Order Date’,fontsize=20)

rolstd.plot(figsize=(20,10), linewidth=3, fontsize=20)

plt.xlabel(‘Order Date’,fontsize=20)

plt.title(‘Rolling Mean & Standard Deviation’)


#Perform Dickey-Fuller test

print (‘Results of Dickey-Fuller Test\n’)

dftest = adfuller(timeseries, autolag=’AIC’)

dfoutput = pd.Series(dftest[0:4], index=[‘Test Statistic’,’p-value’,’#Lags Used’,’Number of bservations Used’])

for key,value in dftest[4].items():

dfoutput[‘Critical Value (%s)’%key] = value



from pylab import rcParams

rcParams[‘figure.figsize’] = 18, 8

decomposition = sm.tsa.seasonal_decompose(ts, model=’additive’)

fig = decomposition.plot()


#Find minimum AIC value

print(“Finding optimal set of parameters\n”)

p = d = q = range(0, 2)

pdq = list(itertools.product(p, d, q))

seasonal_pdq = [(x[0], x[1], x[2], 12) for x in list(itertools.product(p, d, q))]

for param in pdq:

for param_seasonal in seasonal_pdq:


mod = sm.tsa.statespace.SARIMAX(ts,order


results = mod.fit()

print(‘ARIMA{}x{}12 – AIC:{}’.format(param, param_seasonal, results.aic))



#Fit ARIMA model


mod = sm.tsa.statespace.SARIMAX(ts,order=(1, 1, 1),seasonal_order=(1, 1, 0, 12),enforce_stationarity=False,


results = mod.fit()


pred = results.get_prediction(start=pd.to_datetime
(‘2017-01-01’), dynamic=False)

pred_ci = pred.conf_int()

ax = ts[‘2014′:].plot(label=’observed’)

pred.predicted_mean.plot(ax=ax, label=’One-step ahead Forecast’, alpha=.7, figsize=(14, 7))

ax.fill_between(pred_ci.index,pred_ci.iloc[:, 0],pred_ci.iloc[:, 1], color=’k’, alpha=.2)


ax.set_ylabel(‘Furniture Sales’)



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