Modeling of chaotic time series for prediction, interpolation, and smoothing

Abstract

Chaos poses a significant challenge for the time series analyst, since structure in strange attractors tends to be very intricate and nonuniform. Although frequently referred to as unpredictable deterministic behavior, chaotic systems can in fact be forecast over limited time scales. Techniques for constructing predictive models for chaotic dynamics are discussed, including a variety of functional interpolation schemes and several examples of connectionist approaches to the problem. Error estimates based on polynomial interpolation are provided. The underlying deterministic nature of chaotic signals motivates a nonlinear smoothing procedure for the reduction of noise.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>