Physical Review E, 76, 036204p. (2007) DOI:10.1103/PhysRevE.76.036204
Detecting determinism in short time series using a quantified averaged false nearest neighbors approach
S. Ramdani, F. Bouchara, J.-F. CastiesWe 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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