Large sample inference for a multivariate linear model with autocorrelated errors

Abstract

We consider a multivariate linear model with autocorrelated errors. The mean vector of the process is assumed to be linear in the time-trend parameter β and the within-group variation parameter γ. The least-squares estimators of β and γ, and the related estimators of the autoregressive parameter θ and the error covariance matrix Σ are derived and their asymptotic distributions are obtained. Large sample tests of H 1: γ=0 and H 2: β=0are derived and the limit distributions of the restricted least-squares estimators β̂ H 1 and γ̂ H 2 are obtained under H 1 and H 2, respectively.