Detecting determinism in short time series using a quantified averaged false nearest neighbors approach

Sofiane Ramdani, Frédéric Bouchara, and Jean-François Casties
Phys. Rev. E 76, 036204 – Published 12 September 2007

Abstract

We propose a criterion to detect determinism in short time series. This criterion is based on the estimation of the parameter E2 defined by the averaged false neighbors method for analyzing time series [Cao, Physica D 110, 43 (1997)]. Using surrogate data testing with several chaotic and stochastic simulated time series, we show that the variation coefficient of E2 over a few values of the embedding dimension d defines a suitable statistic to detect determinism in short data sequences. This result holds for a time series generated by a high-dimensional chaotic system such as the Mackey-Glass one. Different decreasing lengths of the time series are included in the numerical experiments for both synthetic and real-world data. We also investigate the robustness of the criterion in the case of deterministic time series corrupted by additive noise.

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  • Received 27 April 2007

DOI:https://doi.org/10.1103/PhysRevE.76.036204

©2007 American Physical Society

Authors & Affiliations

Sofiane Ramdani*

  • EA 2991 Efficience et Déficience Motrices, Université de Montpellier I, Montpellier, France

Frédéric Bouchara

  • UMR CNRS 6168 LSIS, Université du Sud Toulon-Var, La Garde, France

Jean-François Casties

  • EA 2991 Efficience et Déficience Motrices, Université de Montpellier I, Montpellier, France

  • *sofiane.ramdani@univ-montp1.fr

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Vol. 76, Iss. 3 — September 2007

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