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

Abstract

The determination of a differential equation underlying a measured time series 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 parameters in a correct type of model, or both. We propose a combination of parametric modelling based on Bock'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 strategy on an experimental time series from a chaotic circuit where we obtain an extremely accurate reconstruction of the observed attractor.

19 pages, 8 Figs

References in corpus (1)

• The identification of continuous, spatiotemporal systems

Cited by in corpus (5)

• Nonparametric inference of interaction laws in systems of agents from trajectory data
• On Statistical Methods of Parameter Estimation for Deterministically Chaotic Time-Series
• Parameter estimation in spatially extended systems: The Karhunen-Loeve and Galerkin multiple shooting approach
• Consistent nonlinear dynamics: identifying model inadequacy
• Nonlinear dynamical models from time series