The Notion of State

Abstract

System theory has shown that the behavior of dynamic systems can be conveniently and succinctly described by introducing the notions of state space and state vectors. Some time series behavior may be so complex that it can’t be described by a finite number of parameters, i.e., its description may go beyond the framework of finite dimensional dynamic models. When a finite dimensional state space model does not suffice to capture time series behavior, we attempt to approximate the series by another of lesser complexity which admits a finite dimensional characterization. In the transform domain description, spectral density functions of finite dimensional dynamics are rational functions of frequencies. They are used to approximate irrational spectral density functions of infinite dimensional dynamics.