ARMAacf {stats} | R Documentation |
Compute the theoretical autocorrelation function or partial autocorrelation function for an ARMA process.
ARMAacf(ar = numeric(0), ma = numeric(0), 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
|
pacf |
logical. Should the partial autocorrelations be returned? |
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.
A vector of (partial) autocorrelations, named by the lags.
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
.
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))