| % File src/library/stats/man/acf.Rd |
| % Part of the R package, https://www.R-project.org |
| % Copyright 1995-2007 R Core Team |
| % Distributed under GPL 2 or later |
| |
| \name{acf} |
| \alias{acf} |
| \alias{ccf} |
| \alias{pacf} |
| \alias{pacf.default} |
| \alias{[.acf} |
| \title{Auto- and Cross- Covariance and -Correlation Function Estimation} |
| \description{ |
| The function \code{acf} computes (and by default plots) estimates of |
| the autocovariance or autocorrelation function. Function \code{pacf} |
| is the function used for the partial autocorrelations. Function |
| \code{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, \dots) |
| |
| pacf(x, lag.max, plot, na.action, \dots) |
| |
| \method{pacf}{default}(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, \dots) |
| |
| \method{[}{acf}(x, i, j) |
| } |
| \arguments{ |
| \item{x, y}{a univariate or multivariate (not \code{ccf}) numeric time |
| series object or a numeric vector or matrix, or an \code{"acf"} object.} |
| \item{lag.max}{maximum lag at which to calculate the acf. |
| Default is \eqn{10\log_{10}(N/m)}{10*log10(N/m)} where \eqn{N} is the |
| number of observations and \eqn{m} the number of series. Will |
| be automatically limited to one less than the number of observations |
| in the series.} |
| \item{type}{character string giving the type of acf to be computed. |
| Allowed values are |
| \code{"correlation"} (the default), \code{"covariance"} or |
| \code{"partial"}. Will be partially matched.} |
| \item{plot}{logical. If \code{TRUE} (the default) the acf is plotted.} |
| \item{na.action}{function to be called to handle missing |
| values. \code{na.pass} can be used.} |
| \item{demean}{logical. Should the covariances be about the sample |
| means?} |
| \item{\dots}{further arguments to be passed to \code{plot.acf}.} |
| |
| \item{i}{a set of lags (time differences) to retain.} |
| \item{j}{a set of series (names or numbers) to retain.} |
| } |
| \value{ |
| An object of class \code{"acf"}, which is a list with the following |
| elements: |
| |
| \item{lag}{A three dimensional array containing the lags at which |
| the acf is estimated.} |
| \item{acf}{An array with the same dimensions as \code{lag} containing |
| the estimated acf.} |
| \item{type}{The type of correlation (same as the \code{type} |
| argument).} |
| \item{n.used}{The number of observations in the time series.} |
| \item{series}{The name of the series \code{x}.} |
| \item{snames}{The series names for a multivariate time series.} |
| |
| The lag \code{k} value returned by \code{ccf(x, y)} estimates the |
| correlation between \code{x[t+k]} and \code{y[t]}. |
| |
| The result is returned invisibly if \code{plot} is \code{TRUE}. |
| } |
| \details{ |
| For \code{type} = \code{"correlation"} and \code{"covariance"}, the |
| estimates are based on the sample covariance. (The lag 0 autocorrelation |
| is fixed at 1 by convention.) |
| |
| By default, no missing values are allowed. If the \code{na.action} |
| function passes through missing values (as \code{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 |
| \code{lag.max}. |
| |
| The generic function \code{plot} has a method for objects of class |
| \code{"acf"}. |
| |
| The lag is returned and plotted in units of time, and not numbers of |
| observations. |
| |
| There are \code{print} and subsetting methods for objects of class |
| \code{"acf"}. |
| } |
| \author{ |
| Original: Paul Gilbert, Martyn Plummer. |
| Extensive modifications and univariate case of \code{pacf} by |
| B. D. Ripley. |
| } |
| \references{ |
| Venables, W. N. and Ripley, B. D. (2002) |
| \emph{Modern Applied Statistics with S}. Fourth Edition. |
| Springer-Verlag. |
| |
| (This contains the exact definitions used.) |
| } |
| |
| \seealso{ |
| \code{\link{plot.acf}}, \code{\link{ARMAacf}} for the exact |
| autocorrelations of a given ARMA process. |
| } |
| \examples{ |
| require(graphics) |
| |
| ## Examples from Venables & Ripley |
| acf(lh) |
| acf(lh, type = "covariance") |
| pacf(lh) |
| |
| acf(ldeaths) |
| acf(ldeaths, ci.type = "ma") |
| acf(ts.union(mdeaths, fdeaths)) |
| ccf(mdeaths, fdeaths, ylab = "cross-correlation") |
| # (just the cross-correlations) |
| |
| presidents # contains missing values |
| acf(presidents, na.action = na.pass) |
| pacf(presidents, na.action = na.pass) |
| } |
| \keyword{ts} |