Bandt-Pompe symbolization dynamics for time series with tied values: a data-driven approach

FRANCISCO TRAVERSARO; FRANCISCO REDELICO; MARCELO RISK; ALEJANDRO FREY; ROSSO, OSVALDO

CHAOS AN INTERDISCIPLINARY JR OF NONLINEAR SCIENCE

AMER INST PHYSICS

Lugar: New York; Año: 2018

1054-1500

Bandt and Pompe introduced in 2002 [Phys. Rev. Lett. 88 (2002) 174102], a successfully symbolic encoding scheme, based on the ordinal relation between the amplitude of neighboring values of a given data sequence, from which the permutation entropy can be evaluated. Equalities in the analyzed sequence, in example, repeated equal values, deserve special attention and treatment as was shown recently by Zunino and coworkers [Phys. Let. A 381 (2017) 1883]. Significant number of equal values can give rise to false conclusions regarding the underlying temporal structures in practical contexts. In the present contribution, we review the different existing methodologies for treats time series with ties values by classifying them according to their different strategies. In addition, a novel data-driven imputation is presented that proves to outperform the existing methodologies and avoiding the false conclusions pointed by Zunino and coworkers.