Auto- and Cross- Covariance and -Correlation Function Estimation
acf computes (and by default plots) estimates of
the autocovariance or autocorrelation function. Function
is the function used for the partial autocorrelations. Function
ccf computes the cross-correlation or cross-covariance of two
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)
- x, y
- a univariate or multivariate (not
ccf) numeric time series object or a numeric vector or matrix, or an
- 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.
- character string giving the type of acf to be computed.
Allowed values are
- logical. If
TRUE(the default) the acf is plotted.
- function to be called to handle missing
na.passcan be used.
- logical. Should the covariances be about the sample means?
- further arguments to be passed to
- a set of lags (time differences) to retain.
- a set of series (names or numbers) to retain.
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
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
The generic function
plot has a method for objects of class
The lag is returned and plotted in units of time, and not numbers of observations.
An object of class
- A three dimensional array containing the lags at which the acf is estimated.
- An array with the same dimensions as
lagcontaining the estimated acf.
- The type of correlation (same as the
- The number of observations in the time series.
- The name of the series
- The series names for a multivariate time series. The lag
"acf", which is a list with the following elements:
kvalue returned by
ccf(x, y)estimates the correlation between
y[t].The result is returned invisibly if
Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. Fourth Edition. Springer-Verlag.
(This contains the exact definitions used.)
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)