ARMAacf
Compute Theoretical ACF for an ARMA Process
Compute the theoretical autocorrelation function or partial autocorrelation function for an ARMA process.
 Keywords
 ts
Usage
ARMAacf(ar = numeric(), ma = numeric(), 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)
, wherep, 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 $0, \dots, max(p, q+1)$, 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
library(stats)
ARMAacf(c(1.0, 0.25), 1.0, lag.max = 10)
## Example from Brockwell & Davis (1991, pp.924)
## 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))
## CovMatrix of length7 subsample of AR(1) example:
toeplitz(ARMAacf(0.8, lag.max = 7))
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