State Space and ARMA Models

Abstract

This chapter establishes the theoretical 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 or observability 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 models of times series for the purposes of either forecasting or analyzing dynamic interdependence of components of the series.