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.

## 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,
demean = TRUE,
...
)
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.

- 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?

- ...
Additional arguments passed to the plotting function.

- y
a univariate numeric time series object or a numeric vector.

- 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.

## Value

The `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".

## 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).

## 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.