LOCAL OPTIMAL METRICS AND NONLINEAR MODELING OF CHAOTIC TIME-SERIES

We consider the problem of prediction and nonlinear modeling for chaot ic time series and examine the effects of changing the local metric us ed to select nearest neighbors in the embedding space of delay registe r vectors. Analyzing simulated numerical data and real data, it is sho wn that the fit achieved for the case where the components of the metr ic tensor are constants over the whole attractor is improved by a prop er selection of the local metric. Our results also suggest how deviati ons from the Euclidean case can be used as a tool to discriminate chao s from correlated noise.