acf {ts}R Documentation

Autocovariance and Autocorrelation 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.

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

Usage

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

plot.acf(acf.obj, ci=0.95, ci.col="blue", ci.type=c("white", "ma"), ...)

Arguments

x, y a univariate or multivariate (not ccf) time series object or a numeric vector or matrix.
lag.max maximum lag at which to calculate the acf. Default is 10*log10(N) where N is the number of observations.
plot logical. If TRUE the acf is plotted.
type character string giving the type of acf to be computed. Allowed values are "correlation" (the default), "covariance" or "partial".
na.action function to be called to handle missing values.
demean logical. Should the covariances be about the sample means?
acf.obj an object of class "acf".
ci coverage probability for confidence interval. Plotting of the confidence interval is suppressed if ci is zero or negative.
ci.col colour to plot the confidence interval lines.
ci.type should the confidence limits assume a white noise input or for lag k an MA(k-1) input?
... graphical parameters.

Details

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

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

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.

Note

The confidence interval plotted in plot.acf is based on an uncorrelated series and should be treated with appropriate caution. Using ci.type = "ma" may be less potentially misleading.

Author(s)

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

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.