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

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 Amigo paradigm of forbidden/missing patterns [J.M. Amigo 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)].