Distinguishing noise from chaos: objective versus subjective criteria using Horizontal Visibility Graph
This work addresses the problem of distinguishing chaos from noise in time series analysis, which is important for researchers in physics and data science, but it is incremental as it builds on and critiques an existing method.
The authors investigated the Horizontal Visibility Graph (HVG) method for distinguishing chaotic from stochastic time series, finding that the original hypothesis about exponential node degree distributions fails in several cases and proposing a new methodology using HVG with Information Theory quantifiers, concluding that the Fisher-Shannon information plane effectively represents the deterministic or stochastic nature of systems.
A recently proposed methodology called the Horizontal Visibility Graph (HVG) [Luque {\it et al.}, Phys. Rev. E., 80, 046103 (2009)] that constitutes a geometrical simplification of the well known Visibility Graph algorithm [Lacasa {\it et al.\/}, Proc. Natl. Sci. U.S.A. 105, 4972 (2008)], has been used to study the distinction between deterministic and stochastic components in time series [L. Lacasa and R. Toral, Phys. Rev. E., 82, 036120 (2010)]. Specifically, the authors propose that the node degree distribution of these processes follows an exponential functional of the form $P(κ)\sim \exp(-λ~κ)$, in which $κ$ is the node degree and $λ$ is a positive parameter able to distinguish between deterministic (chaotic) and stochastic (uncorrelated and correlated) dynamics. In this work, we investigate the characteristics of the node degree distributions constructed by using HVG, for time series corresponding to $28$ chaotic maps and $3$ different stochastic processes. We thoroughly study the methodology proposed by Lacasa and Toral finding several cases for which their hypothesis is not valid. We propose a methodology that uses the HVG together with Information Theory quantifiers. An extensive and careful analysis of the node degree distributions obtained by applying HVG allow us to conclude that the Fisher-Shannon information plane is a remarkable tool able to graphically represent the different nature, deterministic or stochastic, of the systems under study.