R in a Nutshell, 2nd Edition

Autocorrelation Functions

One important property of a time series is the autocorrelation function. You can estimate the autocorrelation function for time series using R’s acf function:

acf(x, lag.max = NULL,
    type = c("correlation", "covariance", "partial"),
    plot = TRUE, na.action = na.fail, demean = TRUE, ...)

The function pacf is an alias for acf, except with the default type of "partial":

pacf(x, lag.max, plot, na.action, ...)

By default, this function plots the results. (An example plot is shown in Plotting Time Series.) As an example, let’s show the autocorrelation function of the turkey price data:

> library(nutshell)
> data(turkey.price.ts)
> acf(turkey.price.ts, plot=FALSE)

Autocorrelations of series ‘turkey.price.ts’, by lag

0.0000 0.0833 0.1667 0.2500 0.3333 0.4167 0.5000 0.5833 0.6667 0.7500 
 1.000  0.465 -0.019 -0.165 -0.145 -0.219 -0.215 -0.122 -0.136 -0.200 
0.8333 0.9167 1.0000 1.0833 1.1667 1.2500 1.3333 1.4167 1.5000 1.5833 
-0.016  0.368  0.723  0.403 -0.013 -0.187 -0.141 -0.180 -0.226 -0.130 

> pacf(turkey.price.ts,plot=FALSE)

Partial autocorrelations of series ‘turkey.price.ts’, by lag

0.0833 0.1667 0.2500 0.3333 0.4167 0.5000 0.5833 0.6667 0.7500 0.8333 
 0.465 -0.300 -0.020 -0.060 -0.218 -0.054 -0.061 -0.211 -0.180  0.098 
0.9167 1.0000 1.0833 1.1667 1.2500 1.3333 1.4167 1.5000 1.5833 
 0.299  0.571 -0.122 -0.077 -0.075  0.119  0.064 -0.149 -0.061

The function ccf plots the cross-correlation function for two time series:

ccf(x, y, lag.max = NULL, type = c("correlation", "covariance"), ...