Causality and the Entropy-Complexity Plane: Robustness and Missing Ordinal Patterns

TL;DR

This paper investigates how to distinguish deterministic signals from noise in time series using entropy-complexity analysis and missing ordinal patterns, especially under noise contamination, demonstrating the robustness of these methods.

Contribution

It extends existing techniques to analyze deterministic time series with correlated noise, showing their effectiveness without extra computations.

Findings

Entropy-complexity plane effectively separates deterministic signals from noise.

Methods remain robust under various noise amplitudes and correlations.

Analysis provides insights into the deterministic component despite noise contamination.

Abstract

We deal here with the issue of determinism versus randomness in time series. One wishes to identify their relative weights in a given time series. Two different tools have been advanced in the literature to such effect, namely, i) the "causal" entropy-complexity plane [Rosso et al. Phys. Rev. Lett. 99 (2007) 154102] and ii) the estimation of the decay rate of missing ordinal patterns [Amig\'o et al. Europhys. Lett. 79 (2007) 50001, and Carpi et al. Physica A 389 (2010) 2020-2029]. In this work we extend the use of these techniques to address the analysis of deterministic finite time series contaminated with additive noises of different degree of correlation. The chaotic series studied here was via the logistic map (r = 4) to which we added correlated noise (colored noise with f-k Power Spectrum, 0 {\leq} k {\leq} 2) of varying amplitudes. In such a fashion important insights pertaining to the deterministic component of the original time series can be gained. We find that in the entropy-complexity plane this goal can be achieved without additional computations.