QUASI-EMPIRICAL BAYES ESTIMATION OF THE PARAMETERS OF AN ARMA(p1, p2) MODEL: SUBSPACE RESTRICTIONS

For the ARMA(p(1), p(2)) model: X-t - theta(1) Xt-1 - ... - theta X-p1(t-p1) = epsilon(t) - alpha(1)epsilon(t-1) - ... - alpha(p2)epsilon(t-p2) where {epsilon(t)} are distributed as i.i.d.N(0, sigma(2)), setting p = p(1) + p(2) we consider the problem of estimation of the p x 1 parameter vector zeta = (theta', alpha')' where theta' = (theta(1),...,theta(p1)) and alpha' = (alpha(1),...,alpha(p2)), when it is suspected that zeta may belong to the subspace H zeta = h, where both the m x p matrix H and the m x 1 vector h consist of constants. Five estimators are defined and their asymptotic distributional bias, M S E matrices, and risk expressions are obtained and compared.