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.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15  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, ...)
## Default S3 method:
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, ...)
## S3 method for class 'acf'
x[i, j]

x, y 
a univariate or multivariate (not 
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

plot 
logical. If 
na.action 
function to be called to handle missing
values. 
demean 
logical. Should the covariances be about the sample means? 
... 
further arguments to be passed to 
i 
a set of lags (time differences) to retain. 
j 
a set of series (names or numbers) to retain. 
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"
.
An object of class "acf"
, which is a list with the following
elements:
lag 
A three dimensional array containing the lags at which the acf is estimated. 
acf 
An array with the same dimensions as 
type 
The type of correlation (same as the 
n.used 
The number of observations in the time series. 
series 
The name of the series 
snames 
The series names for a multivariate time series. 
The lag 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
.
Original: Paul Gilbert, Martyn Plummer.
Extensive modifications and univariate case of pacf
by
B. D. Ripley.
Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. Fourth Edition. SpringerVerlag.
(This contains the exact definitions used.)
plot.acf
, ARMAacf
for the exact
autocorrelations of a given ARMA process.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16  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)

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