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.
acf(x, lag.max = NULL, type = c("correlation", "covariance", "partial"), plot = TRUE, na.action = na.fail, demean = TRUE, ...)
pacf(x, lag.max, plot, na.action, ...)
"pacf"(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, ...)
"["(x, i, j)
ccf
) numeric time
series object or a numeric vector or matrix, or an "acf"
object."correlation"
(the default), "covariance"
or
"partial"
. Will be partially matched.TRUE
(the default) the acf is plotted.na.pass
can be used.plot.acf
."acf"
, which is a list with the following
elements:lag
containing
the estimated acf.type
argument).x
.k
value returned by ccf(x, y)
estimates the
correlation between x[t+k]
and y[t]
.The result is returned invisibly if plot
is TRUE
.
type
= "correlation"
and "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 na.action
function passes through missing values (as 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
lag.max
.
The generic function plot
has a method for objects of class
"acf"
.
The lag is returned and plotted in units of time, and not numbers of observations.
There are print
and subsetting methods for objects of class
"acf"
.
(This contains the exact definitions used.)
plot.acf
, ARMAacf
for the exact
autocorrelations of a given ARMA process.
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)