Quasi-empirical bayes estimation of the parameters of an arma(p1,p2) model: Subspace restrictions

For the arma(p1,p2) model: xt - θ1xt-1-... - θp1 xt-p1 = εt - α1εt-1 -... - αp2εt-p2 where {εt} are distributed as i.i.d.n(0,σ2),setting p = p1 + p2 we consider the problem of estimation of the p × 1 parameter vector ζ= (θ′,α′)′ where θ′ = (θ1,...,θp1) and α′ = (α1,...,αp2),when it is suspected that ζ may belong to the subspace hζ = h,where both the m × p matrix h and the m × 1 vector h consist of constants. five estimators are defined and their asymptotic distributional bias,mse matrices,and risk expressions are obtained and compared. © 2010 pakistan journal of statistics.