# Acf

0th

Percentile

##### (Partial) Autocorrelation and Cross-Correlation Function Estimation

The function Acf computes (and by default plots) an estimate of the autocorrelation function of a (possibly multivariate) time series. Function Pacf computes (and by default plots) an estimate of the partial autocorrelation function of a (possibly multivariate) time series. Function Ccf computes the cross-correlation or cross-covariance of two univariate series.

Keywords
ts
##### Usage
Acf(x, lag.max = NULL, type = c("correlation", "covariance", "partial"), plot = TRUE, na.action = na.contiguous, demean=TRUE, ...)
Pacf(x, lag.max=NULL, plot=TRUE, na.action=na.contiguous, ...)
Ccf(x, y, lag.max=NULL, type=c("correlation","covariance"), plot=TRUE, na.action=na.contiguous, ...)
taperedacf(x, lag.max=NULL, type=c("correlation", "partial"), plot=TRUE, calc.ci=TRUE, level=95, nsim=100, ...)
taperedpacf(x, ...)
##### Arguments
x
a univariate or multivariate (not Ccf) numeric time series object or a numeric vector or matrix.
y
a univariate numeric time series object or a numeric vector.
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 resulting acf, pacf or ccf is plotted.
na.action
function to handle missing values. Default is na.contiguous. Useful alternatives are na.pass and na.interp.
demean
Should covariances be about the sample means?
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 the plotting function.
##### Details

The functions improve the acf, pacf and ccf functions. The main differences are that Acf does not plot a spike at lag 0 when type=="correlation" (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

Acf, Pacf and Ccf 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.

##### See Also

acf, pacf, ccf, tsdisplay

• Acf
• Pacf
• Ccf
• taperedacf
• taperedpacf
##### Examples
Acf(wineind)
Pacf(wineind)
## Not run:
# taperedacf(wineind, nsim=50)
# taperedpacf(wineind, nsim=50)
# ## End(Not run)

Documentation reproduced from package forecast, version 7.3, License: GPL (>= 2)

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