R: Autocovariance and Autocorrelation Function Estimation

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 acf objects.

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\log_{10}(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.