The Notion of State

Abstract

Behavior of dynamic systems can be conveniently and succinctly described by introducing the notions of state space and state vectors. Time series behavior may be so complex that its description may go beyond the framework of finite-dimensional state space, i.e., of finite dimensional dynamic models. When a finite dimensional state space does not suffice to capture time series behavior, then the dynamics are of infinite dimensions. In the transform domain description, spectral density functions of finite dimensional dynamics are rational functions of frequencies. They are irrational functions for infinite dimensional dynamics.