ABSTRACT

These conventional methods are generally ineffective for solving problems such as prediction and filtering for time series produced by nonlinear processes. In particular, a time series measured from a chaotic process typically has a continuous Fourier spectrum instead of a discrete set of frequencies. As a result of this fact, frequency domain methods lack applicability. Time domain methods such as ARMA models become inappropriate because a single global model no longer applies to the entire state space underlying the signal; see Gershenfeld and Weigend (this volume). Some beginning work on state-dependent models for nonlinear signals can be found in Priestley (1988) and Tong (1990).