Application of nonparametric modelling and resampling methods for statistical inference on the structure of multivariate time series

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Inferential analysis about an underlying process based on a measured time series is an inverse problem. Typically, such analysis results in a number that has to be regarded as a realization of a random variable. Therefore, it is of central importance to establish confidence regions for the true values and enable statistical tests to investigate hypotheses about the underlying dynamics. As a basic tool for the implemention of such procedures resampling methods, i.e. methods that are based on the generation of random artificial data sets, have been used in the recent years. In the mathematical and the physics literature two resampling approaches have been developed: The bootstrap in mathematical statistics, and the method of surrogate data in physics. Up to now there has been not much interaction and exchange of ideas between these to fields of research. The aim of the proposed project is to develop a unified mathematical framework for both approaches. Especially, some shortcomings of the surrogate data approach should be solved.