Approximate predictor and filter for partially observed vector ARMA processes (Q1075732)

This is an investigation of approximate \(L_ 2\)-optimal predictor and filter derived for partially observed vector autoregressive moving average processes of order k (ARMA(k,k)) which is a generalization of the result of the author and \textit{G. Michaletzky} [ibid. 11, 321-328 (1985; Zbl 0576.93061)] for an ARMA(1,1) process. As the parameters of \(L_ 2\)-optimal filter seem very complicated the author approximates these parameters neglecting some terms connected with the problem of interpolation. Observability, controllability and stability of the system in question are also discussed.