acf
Auto and Cross Covariance and Correlation Function Estimation
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 crosscorrelation or crosscovariance of two
univariate series.
 Keywords
 ts
Usage
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)
Arguments
 x, y
 a univariate or multivariate (not
ccf
) numeric time series object or a numeric vector or matrix, or an"acf"
object.  lag.max
 maximum lag at which to calculate the acf. Default is $10*log10(N/m)$ where $N$ is the number of observations and $m$ the number of series. Will be automatically limited to one less than the number of observations in the series.
 type
 character string giving the type of acf to be computed.
Allowed values are
"correlation"
(the default),"covariance"
or"partial"
.  plot
 logical. If
TRUE
(the default) the acf is plotted.  na.action
 function to be called to handle missing
values.
na.pass
can be used.  demean
 logical. Should the covariances be about the sample means?
 ...
 further arguments to be passed to
plot.acf
.  i
 a set of lags (time differences) to retain.
 j
 a set of series (names or numbers) to retain.
Details
For 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"
.
Value

An object of class
 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 lag
"acf"
, which is a list with the following
elements: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
.
References
Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. Fourth Edition. SpringerVerlag.
(This contains the exact definitions used.)
See Also
plot.acf
, ARMAacf
for the exact
autocorrelations of a given ARMA process.
Examples
library(stats)
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 = "crosscorrelation")
# (just the crosscorrelations)
presidents # contains missing values
acf(presidents, na.action = na.pass)
pacf(presidents, na.action = na.pass)