On approximate system dynamic

In this paper concepts and techniques from system theory are used to obtain state-space (Markovian ) models of dynamic economic processes instead of the usual VARMA models. In this respect the concept of state is reviewed as are Hankel norm approximations,and balanced realizations for stochastic models. We clarify some aspects of the balancing method for state space modelling of observed time series. This method may fail to satisfy the so-called positive real condition for stochastic processes. We us a state variance factorization algorithm which does not require us to solve the algebraic Riccati equation. We relate the Aoki-Havenner method to the Arun - Kung method