**Autocorrelation** measures the degree of similarity between a time series and a lagged version of itself over successive time intervals.

It’s also sometimes referred to as “serial correlation” or “lagged correlation” since it measures the relationship between a variable’s current values and its historical values.

When the autocorrelation in a time series is high, it becomes easy to predict future values by simply referring to past values.

**How to Calculate Autocorrelation in Python**

Suppose we have the following time series in Python that shows the value of a certain variable during 15 different time periods:

#define data x = [22, 24, 25, 25, 28, 29, 34, 37, 40, 44, 51, 48, 47, 50, 51]

We can calculate the autocorrelation for every lag in the time series by using the acf() function from the statsmodels library:

import statsmodels.api as sm #calculate autocorrelations sm.tsa.acf(x) array([ 1. , 0.83174224, 0.65632458, 0.49105012, 0.27863962, 0.03102625, -0.16527446, -0.30369928, -0.40095465, -0.45823389, -0.45047733])

The way to interpret the output is as follows:

- The autocorrelation at lag 0 is
**1**. - The autocorrelation at lag 1 is
**0.8317**. - The autocorrelation at lag 2 is
**0.6563**. - The autocorrelation at lag 3 is
**0.4910**.

And so on.

We can also specify the number of lags to use with the **nlags **argument:

sm.tsa.acf(x, nlags=5) array([1.0, 0.83174224, 0.65632458, 0.49105012, 0.27863962, 0.03102625])

**How to Plot the Autocorrelation Function in Python**

We can plot the autocorrelation function for a time series in Python by using the tsaplots.plot_acf() function from the statsmodels library:

from statsmodels.graphics import tsaplots import matplotlib.pyplot as plt #plot autocorrelation function fig = tsaplots.plot_acf(x, lags=10) plt.show()

The x-axis displays the number of lags and the y-axis displays the autocorrelation at that number of lags. By default, the plot starts at lag = 0 and the autocorrelation will always be **1 **at lag = 0.

We can also zoom in on the first few lags by choosing to use fewer lags with the **lags **argument:

from statsmodels.graphics import tsaplots import matplotlib.pyplot as plt #plot autocorrelation function fig = tsaplots.plot_acf(x, lags=5) plt.show()

We can also change the title and the color of the circles used in the plot with the **title** and **color** arguments:

from statsmodels.graphics import tsaplots import matplotlib.pyplot as plt #plot autocorrelation function fig = tsaplots.plot_acf(x, lags=5, color='g', title='Autocorrelation function') plt.show()

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