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

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

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?

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

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

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

`arima`

, `ARMAtoMA`

,
`acf2AR`

for inverting part of `ARMAacf`

; further
`filter`

.

# NOT RUN { 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 a.n <- 2^(-n) * (32/3 + 8 * n) /(32/3) (A.n <- ARMAacf(c(1.0, -0.25), 1.0, lag.max = 10)) stopifnot(all.equal(unname(A.n), c(1, a.n))) ARMAacf(c(1.0, -0.25), 1.0, lag.max = 10, pacf = TRUE) zapsmall(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)) # }