General convergence results for maximum likelihood type estimators in multivariable ARMA-models under very weak assumptions are given. This extends results by Dunsmuir and Hannan (1976, Advan. Appl. Probab. 8 339-364) and Deistler, Dunsmuir, and Hannan (1978, Advan. Appl. Probab. 10 360-372). In...

The consistency proof for the (Gaussian quasi) maximum likelihood estimator in multivariable ARMA models as given in Dunsmuir and Hannan (1976, Adv, in Appl. Probab. 8, 339-364) rests on a certain property of the underlying parameter space, called B6 in their paper. It is not known whether the...

The asymptotic properties of maximum likelihood estimates of a vector ARMAX system are considered under general conditions, relating to the nature of the exogenous variables and the innovation sequence and to the form of the parameterization of the rational transfer functions, from exogenous...

The first section of the paper introduces known theory relating to the description of the set of all ARMA structures via the concept of order, n, and the coordinatisation of all structures, M(n), of given order. The coordinates most easily used are related to the state space representation and...