State Space and ARMA Representation

Abstract

This chapter establishes the equivalence of time series model descriptions in terms of well-known ARMA models and less familiar Markovian (state space) models, introduces the notion of minimal dimensional models and the associated minimal dimensional state vectors, and presents several methods for putting models into state space forms in general and into the observable canonical form in particular. Although econometricians and statisticians are perhaps less accustomed to the state space representation of time series, this representation is quite useful in building innovation models of times series.