Chaos and Deterministic versus Stochastic Nonlinear Modeling

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. Nonlinear models are constructed with a variable smoothing parameter which at one extreme defines a nonlinear 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 to dimension calculations.