State space modeling of time series: A review essay

Abstract

The purpose of State Space Modeling of Time Series (SSMTS), as noted by Professor Aoki in his preface, is to serve as a bridge between the systems engineering and econometrics literatures. This timely and important book builds on the earlier work of Aoki (1983) and will be of interest to applied and theoretical econometricians alike. The systems-theoretic flavor of SSMTS, as well as its successes and failures, is well illustrated by the introductory first chapter. There the author argues the virtues of state space (SS) models in terms of their fundamentally multivariate orientation and the fresh insights and perspectives which they furnish (such as the concepts of reachability, observability, balanced representation, and minimal realization). Hankel matrices formed from data autocovariance matrices are emphasized as a unifying theme in model formulation and estimation as well as in prediction. SS model estimation methods based on factorizations of such Hankel matrices are also advocated, This brief chapter successfully whets the appetite for the material of future chapters; at the outset, the reader is promised a substantial return on investment. Some of this return is realized and some is not. SSMTS provides a good overview of systems-theoretic developments of the last twenty years; in addition, a potentially important new technique of analysis and forecasting with