Extraction of Models from Complex Data

In this article we are concerned with the problem of prediction and data reduction of complex dynamical systems1. We will try to answer the following questions: How does one have to choose the delaytime τ and the embedding dimension m, in order to obtain an optimal reconstruction of the strange attractor of a chaotic system from the time series of a single variable? How could one use unstable periodic orbits, in order to extract models that can be used for prediction? What is the optimal encoding of the prediction function?