# Calculating Autocorrelation in R

**R Archives » Data Science Tutorials**, and kindly contributed to R-bloggers]. (You can report issue about the content on this page here)

Want to share your content on R-bloggers? click here if you have a blog, or here if you don't.

The post Calculating Autocorrelation in R appeared first on Data Science Tutorials

Unravel the Future: Dive Deep into the World of Data Science Today! Data Science Tutorials.

Calculating Autocorrelation in R, Autocorrelation is a statistical technique used to measure the degree of similarity between a time series and a lagged version of itself over successive time intervals.

It is also called “serial correlation” or “lagged correlation” since it measures the relationship between a variable’s current and historical values.

In this article, we will explore how to calculate and interpret autocorrelation in R using the `acf()`

function from the `tseries`

library.

**Calculating Autocorrelation**

To calculate the autocorrelation of a time series in R, you can use the `acf()`

function from the `tseries`

library. The basic syntax is as follows:

acf(x, pl=FALSE)

Where `x`

is the time series and `pl=FALSE`

means that the plot will not be displayed. The function returns a vector of autocorrelations for every lag in the time series.

For example, let’s say we have a time series `x`

that shows the value of a certain variable during 15 different periods:

x <- c(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:

Run a specific code block in R » Data Science Tutorials

library(tseries) acf(x, pl=FALSE) Autocorrelations of series ‘x’, by lag 0 1 2 3 4 5 6 7 8 9 10 11 1.000 0.832 0.656 0.491 0.279 0.031 -0.165 -0.304 -0.401 -0.458 -0.450 -0.369

The output will be an autocorrelations vector for every time series lag. The first element of the vector represents the autocorrelation at lag 0 (i.e., the correlation between a value and itself), followed by the autocorrelation at lag 1, then lag 2, and so on.

We can also specify the number of lags to display using the `lag`

argument:

acf(x, lag=5, pl=FALSE) Autocorrelations of series ‘x’, by lag 0 1 2 3 4 5 1.000 0.832 0.656 0.491 0.279 0.031

This will display the autocorrelation up to lag 5.

**Plotting Autocorrelation Function**

We can plot the autocorrelation function for a time series in R by simply not using the `pl=FALSE`

argument:

acf(x)

The resulting plot will display the autocorrelation at each lag on the y-axis and the number of lags on the x-axis. By default, the plot starts at lag = 0, and the autocorrelation will always be 1 at lag = 0.

We can also specify a custom title for the plot using the `main`

argument:

acf(x, main='Autocorrelation by Lag')

**Interpreting Autocorrelation Results**

When interpreting autocorrelation results, it’s essential to consider the following:

- A high autocorrelation at lag 0 indicates that a variable is highly correlated with itself.
- A high autocorrelation at a non-zero lag indicates that there is a significant relationship between current values and past values.
- A low autocorrelation at all lags indicates that there is no significant relationship between current values and past values.

## Conclusion

Calculating and interpreting autocorrelation is an essential step in time series analysis. By using the `acf()`

function in R, you can easily calculate and visualize autocorrelation for your time series data.

- Goodness of Fit Test- Jarque-Bera Test in R
- Combine Rows with Same Column Values in R
- How to Use expand.grid Function in R
- How to Estimate the Efficiency of an Algorithm?
- Need to maintain a good credit score!
- How to Use the scale() Function in R
- How to find the Mean Deviation? MD Vs MAD-Quick Guide
- Self Organizing Maps in R- Supervised Vs Unsupervised

The post Calculating Autocorrelation in R appeared first on Data Science Tutorials

Unlock Your Inner Data Genius: Explore, Learn, and Transform with Our Data Science Haven! Data Science Tutorials.

**leave a comment**for the author, please follow the link and comment on their blog:

**R Archives » Data Science Tutorials**.

R-bloggers.com offers

**daily e-mail updates**about R news and tutorials about learning R and many other topics. Click here if you're looking to post or find an R/data-science job.

Want to share your content on R-bloggers? click here if you have a blog, or here if you don't.