| 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(), 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
|
pacf |
logical. Should the partial autocorrelations be returned? |
Details
The methods used follow
Brockwell and 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 PJ, Davis RA (1991). Time Series: Theory and Methods, series Springer Series in Statistics, Second edition. Springer, New York. ISBN 9780387974293.
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
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))