Estimation and structure determination of multivariate input output systems

Problems associated with the parametric modelling of multivariate input output systems are addressed in this paper. A three stage estimation procedure is proposed, each stage being implemented by means of straighforward closed form multivariate least squares regressions. The statistical properties of the estimates obtained are presented and asymptotic efficiency is achieved. Criteria on the basis of which an appropriate structure can be chosen are advanced and a strategy for the selection of the true or approximating specification is discussed. Consistency when the system can be finitely parameterised is shown.