acf {ts}

R Documentation

Auto- and Cross- Covariance and -Correlation Function Estimation

Description

The function acf computes (and by default plots) estimates of the autocovariance or autocorrelation function. Function pacf is the function used for the partial autocorrelations. Function ccf computes the cross-correlation or cross-covariance of two univariate series.

Usage

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

Arguments

x, y	a univariate or multivariate (not ccf) time series object or a numeric vector or matrix.
lag.max	maximum number of lags at which to calculate the acf. Default is 10\log_{10}(N) where N is the number of observations.
type	character string giving the type of acf to be computed. Allowed values are "correlation" (the default), "covariance" or "partial".
plot	logical. If TRUE the acf is plotted.
na.action	function to be called to handle missing values. na.pass can be used.
demean	logical. Should the covariances be about the sample means?
...	further arguments to be passed to plot.acf.

Details

For type = "correlation" and "covariance", the estimates are based on the sample covariance.

By default, no missing values are allowed. If the na.action function passes through missing values (as na.pass does), the covariances are computed from the complete cases. This means that the estimate computed may well not be a valid autocorrelation sequence, and may contain missing values. Missing values are not allowed when computing the PACF of a multivariate time series.

The partial correlation coefficient is estimated by fitting autoregressive models of successively higher orders up to lag.max.

The generic function plot has a method for objects of class "acf".

The lag is returned and plotted in units of time, and not numbers of observations.

Value

An object of class "acf", which is a list with the following elements:

lag	A three dimensional array containing the lags at which the acf is estimated.
acf	An array with the same dimensions as lag containing the estimated acf.
type	The type of correlation (same as the type argument).
n.used	The number of observations in the time series.
series	The name of the series x.
snames	The series names for a multivariate time series.

The result is returned invisibly if plot is TRUE.

Author(s)

Original: Paul Gilbert, Martyn Plummer. Extensive modifications and univariate case of pacf by B.D. Ripley.

See Also

plot.acf

Examples

## Examples from Venables & Ripley
data(lh)
acf(lh)
acf(lh, type = "covariance")
pacf(lh)

data(UKLungDeaths)
acf(ldeaths)
acf(ldeaths, ci.type = "ma")
acf(ts.union(mdeaths, fdeaths))
ccf(mdeaths, fdeaths) # just the cross-correlations.

data(presidents) # contains missing values
acf(presidents, na.action = na.pass)
pacf(presidents, na.action = na.pass)