**Rolling correlations** are correlations between two time series on a rolling window. One benefit of this type of correlation is that you can visualize the correlation between two time series over time.

This tutorial explains how to calculate and visualize rolling correlations for a pandas DataFrame in Python.

**How to Calculate Rolling Correlations in Pandas**

Suppose we have the following data frame that display the total number of products sold for two different products (*x* and *y*) during a 15-month period:

import pandas as pd import numpy as np #create DataFrame df = pd.DataFrame({'month': np.arange(1, 16), 'x': [13, 15, 16, 15, 17, 20, 22, 24, 25, 26, 23, 24, 23, 22, 20], 'y': [22, 24, 23, 27, 26, 26, 27, 30, 33, 32, 27, 25, 28, 26, 28]}) #view first six rows df.head() month x y 1 1 13 22 2 2 15 24 3 3 16 23 4 4 15 27 5 5 17 26 6 6 20 26

To calculate a rolling correlation in pandas, we can use the rolling.corr() function.

This function uses the following syntax:

**df[‘x’].rolling(width).corr(df[‘y’])**

where:

**df:**Name of the data frame**width:**Integer specifying the window width for the rolling correlation**x, y:**The two column names to calculate the rolling correlation between

Here’s how to use this function to calculate the 3-month rolling correlation in sales between product *x* and product *y*:

#calculate 3-month rolling correlation between sales forxandydf['x'].rolling(3).corr(df['y']) 0 NaN 1 NaN 2 0.654654 3 -0.693375 4 -0.240192 5 -0.802955 6 0.802955 7 0.960769 8 0.981981 9 0.654654 10 0.882498 11 0.817057 12 -0.944911 13 -0.327327 14 -0.188982 dtype: float64

This function returns the correlation between the two product sales for the previous 3 months. For example:

- The correlation in sales during months 1 through 3 was
**0.654654**. - The correlation in sales during months 2 through 4 was
**-0.693375.** - The correlation in sales during months 3 through 5 was
**-0.240192.**

And so on.

We can easily adjust this formula to calculate the rolling correlation for a different time period. For example, the following code shows how to calculate the 6-month rolling correlation in sales between the two products:

#calculate 6-month rolling correlation between sales forxandydf['x'].rolling(6).corr(df['y']) 0 NaN 1 NaN 2 NaN 3 NaN 4 NaN 5 0.558742 6 0.485855 7 0.693103 8 0.756476 9 0.895929 10 0.906772 11 0.715542 12 0.717374 13 0.768447 14 0.454148 dtype: float64

- The correlation in sales during months 1 through 6 was
**0.558742**. - The correlation in sales during months 2 through 7 was
**0.485855.** - The correlation in sales during months 3 through 8 was
**0.693103.**

And so on.

**Notes**

Here are a few notes for the functions used in these examples:

- The
**width**(i.e. the rolling window) should be 3 or greater in order to calculate correlations. - You can find the full documentation for the rolling.corr() function here.

**Additional Resources**

How to Calculate Rolling Correlation in R

How to Calculate Rolling Correlation in Excel