| 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
max(p, q+1), where p, q are the numbers of AR and MA
terms respectively. |
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, ..., 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.
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))