Eur. Phys. J. B (2012) 85: 419
https://doi.org/10.1140/epjb/e2012-30307-8

Regular Article

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

¹ LaCCAN/CPMAT - Instituto de Computação Universidade Federal de Alagoas, BR 104 Norte km 97, 57072-970 Maceió, Alagoas, Brazil
² Laboratorio de Sistemas Complejos, Facultad de Ingeniería. Universidad de Buenos Aires, 1063 Av. Paseo Colón 840, Ciudad Autónoma de Buenos Aires, Argentina
³ Fellow CONICET, 1033 Av. Rivadavia 1917, Buenos Aires, Argentina
⁴ Civil, Surveying and Environmental Engineering. The University of Newcastle, University Drive, Callaghan NSW 2308, Australia
⁵ Departamento de Engenharia de Produção, Universidade Federal de Minas Gerais, Av. Antônio Carlos, 6627, Belo Horizonte, 31270-901 Belo Horizonte - MG, Brazil
⁶ Facultad de Ingeniería, Universidad Nacional de Mar del Plata, Av. J.B. Justo 4302, 7600 Mar del Plata, Argentina
⁷ Universidad Nacional de La Plata, IFLP-CCT, C.C. 727, 1900 La Plata, Argentina
⁸ Universitat de les Illes Balears and IFISC-CSIC, 07122 Palma de Mallorca, Spain

^a e-mail: oarosso@gmail.com

Received: 11 April 2012
Received in final form: 15 September 2012
Published online: 24 December 2012

Abstract

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)].