The Amigó paradigm of forbidden/missing patterns: a detailed analysis

• Published in: The European physical journal. B, Condensed matter physics Vol. 85; no. 12
• Main Authors: Rosso, O. A., Carpi, L. C., Saco, P. M., Ravetti, M. G., Larrondo, H. A., Plastino, A.
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer-Verlag 01-12-2012; EDP Sciences; Springer
• Subjects: Complex Systems; Computational methods in statistical physics and nonlinear dynamics; Condensed Matter Physics; Exact sciences and technology; Fluid- and Aerodynamics; Physics; Physics and Astronomy; Regular Article; Solid State Physics; Statistical physics, thermodynamics, and nonlinear dynamical systems; Statistical and Nonlinear Physics; Deterministic model; Time series; Random effect; Entropy; Probability distribution; Background noise; Distribution functions
• ISSN: 1434-6028; 1434-6036
• DOI: 10.1140/epjb/e2012-30307-8

We deal here with the issue of determinism versus randomness in time series (TS), with the goal of identifying their relative importance in a given TS. To this end we extend (i) the use of ordinal patterns based probability distribution functions associated to a TS [C. Bandt and B. Pompe, Phys. Rev. Lett.
88
, 174102 (2002)] and (ii) the so-called Amigó paradigm of forbidden/missing patterns [J.M. Amigó et al., Europhys. Lett.
79
, 50001 (2007)], to analyze deterministic finite TS contaminated with strong additive noises of different correlation-degree. Useful information on the deterministic component of the original time series is obtained with the help of the so-called causal entropy-complexity plane [O.A. Rosso et al., Phys. Rev. Lett.
99
, 154102 (2007)].