Time series irreversibility: a visibility graph approach

Lacasa Saiz de Arce, Lucas and Nuñez Nuñez, Angel Manuel and Roldán, E. and Parrondo, J.M.R. and Luque Serrano, Bartolome (2012). Time series irreversibility: a visibility graph approach. "The European Physical Journal. B", v. 85 (n. 6); pp. 217-1. ISSN 1434-6028.


Title: Time series irreversibility: a visibility graph approach
  • Lacasa Saiz de Arce, Lucas
  • Nuñez Nuñez, Angel Manuel
  • Roldán, E.
  • Parrondo, J.M.R.
  • Luque Serrano, Bartolome
Item Type: Article
Título de Revista/Publicación: The European Physical Journal. B
Date: 2012
Volume: 85
Freetext Keywords: Statistical and Nonlinear Physics
Faculty: E.T.S.I. Aeronáuticos (UPM)
Department: Matemática Aplicada y Estadística [hasta 2014]
Creative Commons Licenses: Recognition - No derivative works - Non commercial

Full text

PDF - Requires a PDF viewer, such as GSview, Xpdf or Adobe Acrobat Reader
Download (1MB) | Preview


We propose a method to measure real-valued time series irreversibility which combines two different tools: the horizontal visibility algorithm and the Kullback-Leibler divergence. This method maps a time series to a directed network according to a geometric criterion. The degree of irreversibility of the series is then estimated by the Kullback-Leibler divergence (i.e. the distinguishability) between the in and out degree distributions of the associated graph. The method is computationally efficient and does not require any ad hoc symbolization process. We find that the method correctly distinguishes between reversible and irreversible stationary time series, including analytical and numerical studies of its performance for: (i) reversible stochastic processes (uncorrelated and Gaussian linearly correlated), (ii) irreversible stochastic processes (a discrete flashing ratchet in an asymmetric potential), (iii) reversible (conservative) and irreversible (dissipative) chaotic maps, and (iv) dissipative chaotic maps in the presence of noise. Two alternative graph functionals, the degree and the degree-degree distributions, can be used as the Kullback-Leibler divergence argument. The former is simpler and more intuitive and can be used as a benchmark, but in the case of an irreversible process with null net current, the degree-degree distribution has to be considered to identify the irreversible nature of the series

Funding Projects

Comunidad de MadridMODELICOUnspecifiedUnspecifiedUnspecified

More information

Item ID: 16708
DC Identifier: http://oa.upm.es/16708/
OAI Identifier: oai:oa.upm.es:16708
Deposited by: Memoria Investigacion
Deposited on: 13 Nov 2014 16:50
Last Modified: 13 Nov 2014 16:50
  • Open Access
  • Open Access
  • Sherpa-Romeo
    Check whether the anglo-saxon journal in which you have published an article allows you to also publish it under open access.
  • Dulcinea
    Check whether the spanish journal in which you have published an article allows you to also publish it under open access.
  • Recolecta
  • e-ciencia
  • Observatorio I+D+i UPM
  • OpenCourseWare UPM