ARMAacov {tsdecomp} | R Documentation |
Compute Theoretical Autocovariances of an ARMA Model
Description
Compute the theoretical autocovariances of an ARMA model.
Usage
ARMAacov(ar = numeric(0), ma = numeric(0), lag.max = max(p, q + 1),
sigma2 = 1)
Arguments
ar |
numeric vector of AR coefficients. |
ma |
numeric vector of MA coefficients. |
lag.max |
integer, maximum lag to be computed. The default is |
sigma2 |
numeric, the variance of the innovations. |
Value
A vector of autocovariances named by lag order.
Note
Based on ARMAacf
.
References
Brockwell, P. J. and Davis, R. A. (1991) Time Series: Theory and Methods, Second Edition. Springer. doi: 10.1007/978-1-4419-0320-4
Pollock, D. S. G. (1999) A Handbook of Time-Series Analysis Signal Processing and Dynamics. Academic Press. Chapter 17. doi: 10.1016/B978-012560990-6/50002-6
See Also
Examples
# Autocovariances of an ARMA(2,1)
# method 1: using ARMAacov()
a1 <- ARMAacov(ar=c(0.8,-0.6), ma=0.4, lag.max=10)
# method 2: upon the coefficients of the infinite MA representation
psi <- c(1, ARMAtoMA(ar=c(0.8,-0.6), ma=0.4, lag.max=50))
a2 <- c(sum(psi^2), rep(0, length(a1)-1))
for (i in seq_along(a2[-1]))
a2[i+1] <- sum(psi[seq_len(length(psi)-i)] * psi[-seq_len(i)])
# for a high enough number of 'psi' coefficients
# both methods are equivalent
all.equal(a1, a2, check.names=FALSE)
#[1] TRUE
[Package tsdecomp version 0.2 Index]