Combinatorial detection of determinism in noisy time series

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

Research output: Contribution to journalArticlepeer-review


This paper deals with the distinction between white noise and deterministic chaos in multivariate noisy time series. Our method is combinatorial in the sense that it is based on the properties of topological permutation entropy, and it becomes especially interesting when the noise is so high that the standard denoising techniques fail, so a detection of determinism is the most one can hope for. It proceeds by i) counting the number of the so-called ordinal patterns in independent samples of length L from the data sequence and ii) performing a χ2 test based on the results of i), the null hypothesis being that the data are white noise. Holds the null hypothesis, so should all possible ordinal patterns of a given length be visible and evenly distributed over sufficiently many samples, contrarily to what happens in the case of noisy deterministic data. We present numerical evidence in two dimensions for the efficiency of this method. A brief comparison with two common tests for independence, namely, the calculation of the autocorrelation function and the BDS algorithm, is also performed.

Original languageEnglish
Article number60005
Issue number6
Publication statusPublished - Sep 1 2008

ASJC Scopus subject areas

  • Physics and Astronomy(all)


Dive into the research topics of 'Combinatorial detection of determinism in noisy time series'. Together they form a unique fingerprint.

Cite this