Combinatorial detection of determinism in noisy time seriesJ. M. Amigó1, S. Zambrano2 and M. A. F. Sanjuán2
1 Centro de Investigación Operativa, Universidad Miguel Hernández - Avda. de la Universidad s/n., 03202 Elche, Spain, EU
2 Departamento de Física, Universidad Rey Juan Carlos - Tulipán s/n, 28933 Madrid, Spain, EU
received 7 February 2008; accepted in final form 31 July 2008; published September 2008
published online 9 September 2008
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 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.
05.45.Tp - Time series analysis.
05.40.Ca - Noise.
02.50.-r - Probability theory, stochastic processes, and statistics.
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