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.Comment: 19 pages, 8 Fig
