# acf {stats}

### Description

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 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, ...) pacf(x, lag.max, plot, na.action, ...) ## S3 method for class 'default': 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)]

### 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"`

.

### Values

An object of class `"acf"`

, which is a list with the following elements:

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`

.

- 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.

### References

Venables, W. N. and Ripley, B. D. (2002) *Modern Applied Statistics with S*. Fourth Edition. Springer-Verlag.

(This contains the exact definitions used.)

### See Also

`plot.acf`

, `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)

Documentation reproduced from R 3.0.2. License: GPL-2.