# How to Calculate Cross-Correlation in R

How to Calculate Cross-Correlation in R, The degree of resemblance between a time series and a lagged version of another time series is measured using cross-correlation.

In another way, it can tell us whether one-time series is a leading signal for another.

Cross-correlation is used in different areas like economics, business, Biology, etc…

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Some of the common examples are given below.

1) The consumer confidence index (CCI) is regarded as a leading indicator of a country’s gross domestic product (GDP).

2) Marketing spend is sometimes regarded as a leading indicator of a company’s future revenue.

3) The total amount of pollution in the water is thought to be a leading indicator of the population of a particular turtle species.

In this tutorial, we are going to describe how to measure the cross-correlation between two time series in R.

## Cross-Correlation in R

Let’s create a business example suppose the company spends on marketing and the revenue gained in that period.

#create data

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```Spend <- c(5, 3, 6, 5, 8, 9, 10, 17, 12, 11, 10, 9)
Income <- c(25, 29, 22, 34, 22, 28, 29, 31, 34, 45, 45, 40)```

We can calculate the cross-correlation for every lag between the two-time series by using the ccf() function as follows:

measure cross-correlation

`ccf(Spend, Income)` The above plot contains the correlation between the two-time series at various lags.

Obviously, numbers are more important, to get the original correlation values, we can make use of the print function.

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print cross-correlation values

`print(ccf(Spend, Income))`
```Autocorrelations of series ‘X’, by lag
-7     -6     -5     -4     -3     -2     -1      0      1      2      3      4      5      6      7
-0.298 -0.137  0.094  0.475  0.677  0.730  0.607  0.340  0.222 -0.040 -0.226 -0.112 -0.333 -0.228 -0.273```

### Inference

The cross-correlation at lag 0 is 0.340

The cross-correlation at lag 1 is 0.222

The cross-correlation at lag 2 is -0.040

And so on.

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