Local Optimal Metrics and Nonlinear Modeling of Chaotic Time Series

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Abstract
We consider the problem of prediction and nonlinear modeling for chaotic time series and examine the effects of changing the local metric used to select nearest neighbors in the embedding space of delay register vectors. Analyzing simulated numerical data and real data, it is shown that the fit achieved for the case where the components of the metric tensor are constants over the whole attractor is improved by a proper selection of the local metric. Our results also suggest how deviations from the Euclidean case can be used as a tool to discriminate chaos from correlated noise.