Testing time series irreversibility using complex network methods

The absence of time-reversal symmetry is a fundamental property of many nonlinear time series. Here, we propose a new set of statistical tests for time series irreversibility based on standard and horizontal visibility graphs. Specifically, we statistically compare the distributions of time-directed variants of the common complex network measures degree and local clustering coefficient. Our approach does not involve surrogate data and is applicable to relatively short time series. We demonstrate its performance for paradigmatic model systems with known time-reversal properties as well as for picking up signatures of nonlinearity in neuro-physiological data.

[1]  J. M. R. Parrondo,et al.  Time series irreversibility: a visibility graph approach , 2012 .

[2]  C. Diks.  Nonlinear time series analysis , 1999 .

[3]  J. C. Nuño,et al.  The visibility graph: A new method for estimating the Hurst exponent of fractional Brownian motion , 2009, 0901.0888.

[4]  Michael Small,et al.  Superfamily phenomena and motifs of networks induced from time series , 2008, Proceedings of the National Academy of Sciences.

[5]  Lucas Lacasa,et al.  From time series to complex networks: The visibility graph , 2008, Proceedings of the National Academy of Sciences.

[6]  M Small,et al.  Complex network from pseudoperiodic time series: topology versus dynamics. , 2006, Physical review letters.

[7]  Chung-Kang Peng,et al.  Broken asymmetry of the human heartbeat: loss of time irreversibility in aging and disease. , 2005 .

[8]  E. Ryabov,et al.  Intramolecular vibrational redistribution: from high-resolution spectra to real-time dynamics , 2012 .

[9]  Zhi-Qiang Jiang,et al.  Universal and nonuniversal allometric scaling behaviors in the visibility graphs of world stock market indices , 2009, 0910.2524.

[10]  J. Kurths,et al.  Complex network approach for recurrence analysis of time series , 2009, 0907.3368.

[11]  B. Luque,et al.  Horizontal visibility graphs: exact results for random time series. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[12]  K Lehnertz,et al.  Indications of nonlinear deterministic and finite-dimensional structures in time series of brain electrical activity: dependence on recording region and brain state. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[13]  H. Tong.  Non-linear time series. A dynamical system approach , 1990 .

[14]  Jürgen Kurths,et al.  Recurrence networks—a novel paradigm for nonlinear time series analysis , 2009, 0908.3447.

[15]  Luciano Telesca,et al.  Analysis of seismic sequences by using the method of visibility graph , 2012 .

[16]  Juan M R Parrondo,et al.  Estimating dissipation from single stationary trajectories. , 2010, Physical review letters.

[17]  宁北芳,et al.  疟原虫var基因转换速率变化导致抗原变异[英]／Paul H, Robert P, Christodoulou Z, et al//Proc Natl Acad Sci U S A , 2005 .

[18]  A. Porporato,et al.  Irreversibility and fluctuation theorem in stationary time series. , 2007, Physical review letters.

[19]  Matthew B Kennel,et al.  Testing time symmetry in time series using data compression dictionaries. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[20]  Cees Diks,et al.  Reversibility as a criterion for discriminating time series , 1995 .