(Partial) Autocorrelation Function Estimation
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.
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, ...)
- a univariate time series
- 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
correlation" (the default) or "
- logical. If TRUE (the default) the acf is plotted.
- Title for plot
- The x limits of the plot
- The y limits of the plot
- The label on the x-axis of the plot
- The label on the y-axis of the plot
- function to handle missing values. Default is
na.contiguous. Useful alternatives are
TRUE, confidence intervals for the ACF/PACF estimates are calculated.
- Percentage level used for the confidence intervals.
- The number of bootstrap samples used in estimating the confidence intervals.
- Additional arguments passed to
acfor to the plotting function.
The functions improve the
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).
Pacffunctions return objects of class "acf" as described in
acffrom the stats package. The
taperedpacffunctions return objects of class "mpacf".
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(wineind) Pacf(wineind) taperedacf(wineind, nsim=50) taperedpacf(wineind, nsim=50)