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

O. A. ROSSO; L. C. CARPI; P. M. SACO; M. GÓMEZ RAVETTI; A. PLASTINO; H. A. LARRONDO

PHYSICA A - STATISTICAL AND THEORETICAL PHYSICS

ELSEVIER SCIENCE BV

Año: 2012 vol. 391 p. 42 - 55

0378-4371

We deal here with the issue of determinism versus randomness intime series. One wishes to identify their relative weights in agiven time series. Two different tools have been advanced in theliterature 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 ofmissing ordinal patterns [Amigó   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 techniquesto address the analysis of deterministic finite time seriescontaminated with additive noises of different degree of correlation. Thechaotic series studied here was via the logistic map (r=4) towhich we added correlated noise (colored noise with f^{-k}PowerSpectrum, 0 leq k leq 2) of varying amplitudes. In such afashion important insights pertaining to the deterministiccomponent of the original time series can be gained. We find thatin the entropy-complexity plane  this goal can be achievedwithout additional computations.