tccfAR: Theoretical cross-covariances of auxilary AR process in ARMA(p,q)
Description
The auxilary AR processes in the ARMA(p,q) model phi(B)z(t)=theta(B)a(t) are defined by
phi(B)u(t)=-a(t) and theta(B)v(t)=a(t).
The upper off-diagonal p-by-q block of the ARMA information matrix is obtained
from the cross-covariances of u(t) and v(t).
This function obtains these covariances.
Usage
tccfAR(phi, theta)
Arguments
phi
AR coefficients in ARMA
theta
MA coefficients in ARMA
Value
vector of cross-covariances
Details
A set of linear equations which determine the covariances is solved.
The algorithm is similar in spirit to that for the autocovariances (McLeod, 1975).
References
McLeod, A.I. (1975),
Derivation of the theoretical autocorrelation function of autoregressive
moving-average time series,
Applied Statistics 24, 255-256.