Detecting determinism in time series with ordinal patterns: A comparative study

J. M. Amigó, S. Zambrano, M. A F Sanjuán

Research output: Contribution to journalArticle


Detecting determinism in univariate and multivariate time series is difficult if the underlying process is nonlinear, and the noise level is high. In a previous paper, the authors proposed a method based on observable ordinal patterns. This method exploits the robustness of admissible ordinal patterns against observational noise, and the super-exponential growth of forbidden ordinal patterns with the length of the patterns. The new method compared favorably to the BrockDechertScheinkman independence test when applied to time series projected from the Hénon attractor and contaminated with Gaussian noise of different variances. In this paper, we extend this comparison to higher fractal dimensions by using noisy orbits on the attractors of the Lorenz map, and the time-delayed Hénon map. Finally, we make an analysis that enlightens the robustness of admissible ordinal patterns in the presence of observational noise.

Original languageEnglish
Pages (from-to)2915-2924
Number of pages10
JournalInternational Journal of Bifurcation and Chaos
Issue number9
Publication statusPublished - Sep 2010


  • BDS test
  • independence test
  • Ordinal patterns
  • permutation entropy

ASJC Scopus subject areas

  • Applied Mathematics
  • General
  • Engineering(all)
  • Modelling and Simulation

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