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Abstract: In the nonlinear prediction of scalar time series, the common practice is toreconstruct the state space using time-delay embedding and apply a local modelon neighborhoods of the reconstructed space. The method of false nearestneighbors is often used to estimate the embedding dimension. For predictionpurposes, the optimal embedding dimension can also be estimated by someprediction error minimization criterion. We investigate the proper state spacereconstruction for multivariate time series and modify the two abovementionedcriteria to search for optimal embedding in the set of the variables and theirdelays. We pinpoint the problems that can arise in each case and compare thestate space reconstructions suggested by each of the two methods on thepredictive ability of the local model that uses each of them. Results obtainedfrom Monte Carlo simulations on known chaotic maps revealed the non-uniquenessof optimum reconstruction in the multivariate case and showed that predictioncriteria perform better when the task is prediction.



Author: I. Vlachos, D. Kugiumtzis

Source: https://arxiv.org/



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