Parametric, nonparametric and parametric modelling of a chaotic circuit time series

The determination of a differential equation underlying a measured time ser ies is a frequently arising task in nonlinear time series analysis. In the validation of a proposed model one often faces the dilemma that it is hard to decide whether possible discrepancies between the time series and model output are caused by an inappropriate model or by bad estimates of paramete rs in a correct type of model, or both. We propose a combination of paramet ric modelling based on Beck's multiple shooting algorithm and nonparametric modelling based on optimal transformations as a strategy to test proposed models and if rejected suggest and test new ones. We exemplify this strateg y on an experimental time series from a chaotic circuit where we obtain an extremely accurate reconstruction of the observed attractor. (C) 2000 Elsev ier Science B.V. All rights reserved.