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\name{acf}
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\name{acf}
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\alias{acf}
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\alias{acf}
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\alias{ccf}
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\alias{ccf}
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\alias{pacf}
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\alias{pacf}
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\alias{pacf.default}
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\alias{pacf.default}
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\alias{[.acf}
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\title{Auto- and Cross- Covariance and -Correlation Function Estimation}
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\title{Auto- and Cross- Covariance and -Correlation Function Estimation}
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\description{
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\description{
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  The function \code{acf} computes (and by default plots) estimates of
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  The function \code{acf} computes (and by default plots) estimates of
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  the autocovariance or autocorrelation function.  Function \code{pacf}
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  the autocovariance or autocorrelation function.  Function \code{pacf}
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  is the function used for the partial autocorrelations.  Function
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  is the function used for the partial autocorrelations.  Function
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\method{pacf}{default}(x, lag.max = NULL, plot = TRUE, na.action = na.fail,
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\method{pacf}{default}(x, lag.max = NULL, plot = TRUE, na.action = na.fail,
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    ...)
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    ...)
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ccf(x, y, lag.max = NULL, type = c("correlation", "covariance"),
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ccf(x, y, lag.max = NULL, type = c("correlation", "covariance"),
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    plot = TRUE, na.action = na.fail, \dots)
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    plot = TRUE, na.action = na.fail, \dots)
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acf.obj[i, j]
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}
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}
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\arguments{
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\arguments{
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  \item{x, y}{a univariate or multivariate (not \code{ccf}) numeric time
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  \item{x, y}{a univariate or multivariate (not \code{ccf}) numeric time
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    series object or a numeric vector or matrix.}
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    series object or a numeric vector or matrix.}
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  \item{lag.max}{maximum number of lags at which to calculate the acf.
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  \item{lag.max}{maximum number of lags at which to calculate the acf.
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  \item{na.action}{function to be called to handle missing
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  \item{na.action}{function to be called to handle missing
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    values. \code{na.pass} can be used.}
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    values. \code{na.pass} can be used.}
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  \item{demean}{logical.  Should the covariances be about the sample
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  \item{demean}{logical.  Should the covariances be about the sample
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    means?}
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    means?}
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  \item{\dots}{further arguments to be passed to \code{plot.acf}.}
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  \item{\dots}{further arguments to be passed to \code{plot.acf}.}
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  \item{acf.obj}{an object of class \code{"acf"} resulting from a call
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    to \code{acf}.}
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  \item{i}{a set of lags to retain.}
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  \item{j}{a set of series to retain.}
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}
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}
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\value{
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\value{
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  An object of class \code{"acf"}, which is a list with the following
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  An object of class \code{"acf"}, which is a list with the following
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  elements:
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  elements:
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  The generic function \code{plot} has a method for objects of class
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  The generic function \code{plot} has a method for objects of class
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  \code{"acf"}.
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  \code{"acf"}.
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  The lag is returned and plotted in units of time, and not numbers of
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  The lag is returned and plotted in units of time, and not numbers of
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  observations.
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  observations.
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  There are \code{print} and subsetting methods for objects of class
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  \code{"acf"}.
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}
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}
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\author{
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\author{
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  Original: Paul Gilbert, Martyn Plummer.
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  Original: Paul Gilbert, Martyn Plummer.
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  Extensive modifications and univariate case of \code{pacf} by
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  Extensive modifications and univariate case of \code{pacf} by
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  B.D. Ripley.
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  B.D. Ripley.