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% File src/library/stats/man/ARMAacf.Rd
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% File src/library/stats/man/ARMAacf.Rd
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% Part of the R package, https://www.R-project.org
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% Part of the R package, https://www.R-project.org
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% Copyright 1995-2015 R Core Team
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% Copyright 1995-2025 R Core Team
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% Distributed under GPL 2 or later
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% Distributed under GPL 2 or later
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\name{ARMAacf}
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\name{ARMAacf}
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\alias{ARMAacf}
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\alias{ARMAacf}
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\title{Compute Theoretical ACF for an ARMA Process}
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\title{Compute Theoretical ACF for an ARMA Process}
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    terms respectively.}
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    terms respectively.}
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  \item{pacf}{logical.  Should the partial autocorrelations be returned?}
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  \item{pacf}{logical.  Should the partial autocorrelations be returned?}
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}
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}
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\details{
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\details{
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  The methods used follow
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  The methods used follow
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  \bibcite{Brockwell & Davis (1991, section 3.3)}.  Their
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  \bibcitet{|R:Brockwell+Davis:1991|section 3.3}.  Their
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  equations (3.3.8) are solved for the autocovariances at lags
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  equations (3.3.8) are solved for the autocovariances at lags
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  \eqn{0, \dots, \max(p, q+1)}{0, \dots, max(p, q+1)},
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  \eqn{0, \dots, \max(p, q+1)}{0, \dots, max(p, q+1)},
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  and the remaining autocorrelations are given by a recursive filter.
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  and the remaining autocorrelations are given by a recursive filter.
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}
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}
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\value{
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\value{
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  A vector of (partial) autocorrelations, named by the lags.
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  A vector of (partial) autocorrelations, named by the lags.
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}
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}
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\references{
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\references{
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  Brockwell, P. J. and Davis, R. A. (1991) \emph{Time Series: Theory and
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    Methods}, Second Edition.  Springer.
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  \bibshow{*}
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}
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}
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\seealso{\code{\link{arima}}, \code{\link{ARMAtoMA}},
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\seealso{\code{\link{arima}}, \code{\link{ARMAtoMA}},
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  \code{\link{acf2AR}} for inverting part of \code{ARMAacf}; further
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  \code{\link{acf2AR}} for inverting part of \code{ARMAacf}; further
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  \code{\link{filter}}.
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  \code{\link{filter}}.
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}
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}