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The problem considered is that of approximation to the structure of the stationary process generating a vector time series by a rational transfer function, i.e. ARMA, system. The structure of such systems and their coordinatization are discussed together with some deterministic approximation theory. Criteria on the basis of which to choose an approximant are considered. Theorems supporting such criteria and describing the properties of approximants are given. Finally some algorithms are described including algorithms for real time calculation of the estimates.
E. J. Hannan (Fri,) studied this question.