Optimal Markov Approximations and Generalized Embeddings

Details Optimal Markov Approximations and Generalized Embeddings Optimal Markov Approximations and Generalized Embeddings

2008-08-11

arxiv.org/abs/0808.1513v1

Nonlinear Sciences

Chaotic Dynamics

12 pages, 6 figures

Scientific paper

Based on information theory, we present a method to determine an optimal Markov approximation for modelling and prediction from time series data. The method finds a balance between minimal modelling errors by taking as much as possible memory into account and minimal statistical errors by working in embedding spaces of rather small dimension. A key ingredient is an estimate of the statistical error of entropy estimates. The method is illustrated with several examples and the consequences for prediction are evaluated by means of the root mean squard prediction error for point prediction.

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