In this lab, you'll practice your knowledge of testing for stationarity.

You will be able to:

• Check and comment on the stationarity of time series data
• Use rolling statistics as an initial check for stationarity
• Use the Dickey-Fuller Test for performing statistical testing for time series stationarity

Let's look at some new data. In this lab, We'll work by creating a time-series object in Python by using the popular Air Passengers dataset.

This dataset is stored as passengers.csv.

# Import necessary libraries

Import passengers.csv and view the head.

# Read the dataset 'passengers.csv' and view the head

# Month	#Passengers
# 0	1949-01-01	112
# 1	1949-02-01	118
# 2	1949-03-01	132
# 3	1949-04-01	129
# 4	1949-05-01	121

Change the Month column over to a datetime object and make sure it is set as the index.

# Set month column as a timeseries object, and make it the index

# check the head and the new index


# DatetimeIndex(['1949-01-01', '1949-02-01', '1949-03-01', '1949-04-01',
#                '1949-05-01', '1949-06-01', '1949-07-01', '1949-08-01',
#                '1949-09-01', '1949-10-01',
#                ...
#                '1960-03-01', '1960-04-01', '1960-05-01', '1960-06-01',
#                '1960-07-01', '1960-08-01', '1960-09-01', '1960-10-01',
#                '1960-11-01', '1960-12-01'],
#               dtype='datetime64[ns]', name='Month', length=144, freq=None)

Now that we have successfully created a TS object, we can use the plot() function in pandas to visually inspect this time-series.

# Plot the time series data 

Wec can see that that there is an overall increasing trend in the data along with some seasonal variations. However, it might not always be possible to make such visual inferences. Let's reconfirm this here using both rolling statistics and the Dickey-Fuller Test.

Use the .rolling() function to find the rolling mean and rolling std with a window of 12 months. Plot the original curve along with the rolling mean and standard error.

#Determine rolling statistics

#Plot rolling statistics

Though the variation in standard deviation is small, the mean is increasing with time and thus, this is not a stationary series.

Use the Dickey-Fuller Test to verify your visual result.

from statsmodels.tsa.stattools import adfuller

#Perform Dickey-Fuller test:

# Extract and display test results in a user friendly manner

# 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 (1%)             -3.481682
# Critical Value (5%)             -2.884042
# Critical Value (10%)            -2.578770
# dtype: float64

Repeat the previous steps for the NYSE monthly data , stored in "NYSE_monthly.csv".

In this lab, you learned to check for the stationarity of a time-series object in Python. Next, we'll further explore stationarity and how to make sure to make time series stationary!