Noisy-chaotic time series and the forbidden/missing patterns paradigm

TL;DR

This paper extends ordinal pattern analysis and forbidden pattern paradigms to distinguish deterministic signals from noise in time series, even under strong additive noise contamination, using entropy-complexity measures.

Contribution

It introduces an enhanced framework combining ordinal patterns and forbidden patterns with entropy measures to analyze noisy deterministic time series.

Findings

Effective discrimination between deterministic and stochastic components.

Robust analysis under high noise levels.

Insights into the deterministic structure despite noise contamination.

Abstract

We deal here with the issue of determinism versus randomness in time series. One wishes to identify their relative importance in a given time series. To this end we extend i) the use of ordinal patterns-based probability distribution functions associated with a time series [Bandt and Pompe, Phys. Rev. Lett. 88 (2002) 174102] and ii) the so-called Amig\'o paradigm of forbidden/missing patterns [Amig\'o, Zambrano, Sanju\'an, Europhys. Lett. 79 (2007) 50001], to analyze deterministic finite time series contaminated with strong additive noises of different correlation-degree. Insights pertaining to the deterministic component of the original time series are obtained with the help of the causal entropy-complexity plane [Rosso et al. Phys. Rev. Lett. 99 (2007) 154102].