# Acf

0th

Percentile

##### (Partial) Autocorrelation Function Estimation

The function Acf computes (and by default plots) an estimate of the autocorrelation function of a univariate time series. Function Pacf computes (and by default plots) an estimate of the partial autocorrelation function of a univariate time series.

Keywords
ts
##### Usage
Acf(x, lag.max=NULL, type=c("correlation", "partial"),
plot=TRUE, main=NULL, xlim=NULL, ylim=NULL, xlab="Lag", ylab=NULL,
na.action=na.contiguous, ...)
Pacf(x, main=NULL, ...)
taperedacf(x, lag.max=NULL, type=c("correlation", "partial"),
plot=TRUE, calc.ci=TRUE, level=95, nsim=100,
xlim=NULL, ylim=NULL, xlab="Lag",  ylab=NULL, ...)
taperedpacf(x, ...)
##### Arguments
x
a univariate time series
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) or "partial".
plot
logical. If TRUE (the default) the acf is plotted.
main
Title for plot
xlim
The x limits of the plot
ylim
The y limits of the plot
xlab
The label on the x-axis of the plot
ylab
The label on the y-axis of the plot
na.action
function to handle missing values. Default is na.contiguous. Useful alternatives are na.pass and na.
calc.ci
If TRUE, confidence intervals for the ACF/PACF estimates are calculated.
level
Percentage level used for the confidence intervals.
nsim
The number of bootstrap samples used in estimating the confidence intervals.
...
Additional arguments passed to acf or to the plotting function.
##### Details

The functions improve the acf and pacf functions when applied to univariate time series. The main differences are that Acf does not plot a spike at lag 0 (which is redundant) and the horizontal axes show lags in time units rather than seasonal units.

The tapered versions implement the ACF and PACF estimates and plots described in Hyndman (2015), based on the banded and tapered estimates of autocovariance proposed by McMurry and Politis (2010).

##### Value

• The Acf and Pacf functions return objects of class "acf" as described in acf from the stats package. The taperedacf and taperedpacf functions return objects of class "mpacf".

##### References

Hyndman, R.J. (2015). Discussion of High-dimensional autocovariance matrices and optimal linear prediction''. Electronic Journal of Statistics, 9, 792-796.

McMurry, T. L., & Politis, D. N. (2010). Banded and tapered estimates for autocovariance matrices and the linear process bootstrap. Journal of Time Series Analysis, 31(6), 471-482.

acf, pacf, tsdisplay

• Acf
• Pacf
• taperedacf
• taperedpacf
##### Examples
Acf(wineind)
Pacf(wineind)
taperedacf(wineind, nsim=50)
taperedpacf(wineind, nsim=50)
Documentation reproduced from package forecast, version 6.0, License: GPL (>= 2)

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