title: Detecting determinism in short time series using a quantified averaged false nearest neighbors approach.
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.
authors.affiliation: EA 2991 Efficience et Déficience Motrices, Université de Montpellier I, Montpellier, France. sofiane.ramdani@univ-montp1.fr
authors.forename: Sofiane
authors.initials: S
authors.lastname: Ramdani
authors.forename: Frédéric
authors.initials: F
authors.lastname: Bouchara
authors.forename: Jean-François
authors.initials: JF
authors.lastname: Casties