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We develop a method for estimating closed-form nonlinear dynamical models from observed time series, which expresses the unknown coefficients as functions of generalized higher-order data correlations. Besides robust numerical properties, this method often yields analytic coefficient representations which provide theoretical insight into general model properties.

Classification of time series using a dynamical system ansatz is potentially powerful, however assessing performance for noisy experimental data is problematic. Here, we develop a rigorous statistical framework for calculating classification probabilities using global dynamical models, and analytically derive some asymptotic properties. We illustrate the method numerically by attempting to detect “determinism” in a noisy data set.