ARMAacf {stats} | R Documentation |

## Compute Theoretical ACF for an ARMA Process

### Description

Compute the theoretical autocorrelation function or partial
autocorrelation function for an ARMA process.

### Usage

ARMAacf(ar = numeric(0), ma = numeric(0), lag.max = r, pacf = FALSE)

### Arguments

`ar` |
numeric vector of AR coefficients |

`ma` |
numeric vector of MA coefficients |

`lag.max` |
integer. Maximum lag required. Defaults to
`max(p, q+1)` , where `p, q` are the numbers of AR and MA
terms respectively. |

`pacf` |
logical. Should the partial autocorrelations be returned? |

### Details

The methods used follow Brockwell & Davis (1991, section 3.3). Their
equations (3.3.8) are solved for the autocovariances at lags
*0, ..., max(p, q+1)*, and the remaining autocorrelations are
given by a recursive filter.

### Value

A vector of (partial) autocorrelations, named by the lags.

### References

Brockwell, P. J. and Davis, R. A. (1991) *Time Series: Theory and
Methods*, Second Edition. Springer.

### See Also

`arima`

, `ARMAtoMA`

,
`acf2AR`

for inverting part of `ARMAacf`

; further
`filter`

.

### Examples

ARMAacf(c(1.0, -0.25), 1.0, lag.max = 10)
## Example from Brockwell & Davis (1991, pp.92-4)
## answer 2^(-n) * (32/3 + 8 * n) /(32/3)
n <- 1:10; 2^(-n) * (32/3 + 8 * n) /(32/3)
ARMAacf(c(1.0, -0.25), 1.0, lag.max = 10, pacf = TRUE)
ARMAacf(c(1.0, -0.25), lag.max = 10, pacf = TRUE)
## Cov-Matrix of length-7 sub-sample of AR(1) example:
toeplitz(ARMAacf(0.8, lag.max = 7))

[Package

*stats* version 2.5.0

Index]