Autocorrelation and Partial autocorrelation

Visualizing Time Series Data in Python

Thomas Vincent

Head of Data Science, Getty Images

Autocorrelation in time series data

Autocorrelation is measured as the correlation between a time series and a delayed copy of itself
For example, an autocorrelation of order 3 returns the correlation between a time series at points (t_1, t_2, t_3, ...) and its own values lagged by 3 time points, i.e. (t_4, t_5, t_6, ...)
It is used to find repetitive patterns or periodic signal in time series

Statsmodels

statsmodels is a Python module that provides classes and functions for the estimation of many different statistical models, as well as for conducting statistical tests, and statistical data exploration.

Plotting autocorrelations

import matplotlib.pyplot as plt
from statsmodels.graphics import tsaplots
fig = tsaplots.plot_acf(co2_levels['co2'], lags=40)

plt.show()

Interpreting autocorrelation plots

Autocorrelation in time series

Partial autocorrelation in time series data

Contrary to autocorrelation, partial autocorrelation removes the effect of previous time points
For example, a partial autocorrelation function of order 3 returns the correlation between our time series (t1, t2, t3, ...) and lagged values of itself by 3 time points (t4, t5, t6, ...), but only after removing all effects attributable to lags 1 and 2

Plotting partial autocorrelations

import matplotlib.pyplot as plt

from statsmodels.graphics import tsaplots
fig = tsaplots.plot_pacf(co2_levels['co2'], lags=40)

plt.show()

Interpreting partial autocorrelations plot

Partial Autocorrelation in time series

Let's practice!

Visualizing Time Series Data in Python