Chaos and Deterministic <i>Versus</i> Stochastic Non-Linear Modelling

Abstract

SUMMARY An exploratory technique is introduced for investigating how much of the irregularity in an aperiodic time series is due to low dimensional chaotic dynamics, as opposed to stochastic or high dimensional dynamics. Non-linear models are constructed with a variable smoothing parameter which at one extreme defines a non-linear deterministic model, and at the other extreme defines a linear stochastic model. The accuracy of the resulting short-term forecasts as a function of the smoothing parameter reveals much about the underlying dynamics generating the time series. The technique is applied to a variety of experimental and naturally occurring time series data, and the results are compared with dimension calculations.