**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 rolling correlations in R.

**How to Calculate Rolling Correlations in R**

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:

#create data data <- data.frame(month=1:15, x=c(13, 15, 16, 15, 17, 20, 22, 24, 25, 26, 23, 24, 23, 22, 20), y=c(22, 24, 23, 27, 26, 26, 27, 30, 33, 32, 27, 25, 28, 26, 28)) #view first six rows head(data) 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 R, we can use the rollapply() function from the **zoo** package.

This function uses the following syntax:

**rollapply(data, width, FUN, by.column=TRUE)**

where:

**data:**Name of the data frame**width:**Integer specifying the window width for the rolling correlation**FUN:**The function to be applied.**by.column:**Specifies whether to apply the function to each column separately. This is TRUE by default, but to calculate a rolling correlation we need to specify this to be FALSE.

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 forxandyrollapply(data, width=3, function(x) cor(x[,2],x[,3]), by.column=FALSE) [1] 0.6546537 -0.6933752 -0.2401922 -0.8029551 0.8029551 0.9607689 [7] 0.9819805 0.6546537 0.8824975 0.8170572 -0.9449112 -0.3273268 [13] -0.1889822

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
**0.6546537**. - The correlation in sales during months 2 through 4 was
**-0.6933752.** - The correlation in sales during months 3 through 5 was
**-0.2401922.**

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 forxandyrollapply(data, width=6, function(x) cor(x[,2],x[,3]), by.column=FALSE) [1] 0.5587415 0.4858553 0.6931033 0.7564756 0.8959291 0.9067715 0.7155418 [8] 0.7173740 0.7684468 0.4541476

This function returns the correlation between the two product sales for the previous 6 months. For example:

- The correlation in sales during months 1 through 6 was
**0.5587415**. - The correlation in sales during months 2 through 7 was
**0.4858553.** - The correlation in sales during months 3 through 8 was
**0.6931033.**

And so on.

**Notes**

Keep the following in mind when using the rollapply() function:

- The
**width**(i.e. the rolling window) should be 3 or greater in order to calculate correlations. - In the formulas above, we used cor(x[,2],x[3]) because the two columns that we wanted to calculate correlations between were in position
**2**and**3**. Adjust these numbers if the columns you’re interested in are located in different positions.