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Phys Rev E Stat Nonlin Soft Matter Phys. 2015 Feb;91(2):022926. Epub 2015 Feb 27.

Analyzing long-term correlated stochastic processes by means of recurrence networks: potentials and pitfalls.

Zou Y1,2,3, Donner RV3, Kurths J3,4,5,6.

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Department of Physics, East China Normal University, 200062 Shanghai, China.
State Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, China.
Potsdam Institute for Climate Impact Research, P. O. Box 60 12 03, 14412 Potsdam, Germany.
Department of Physics, Humboldt University Berlin, Newtonstraße 15, 12489 Berlin, Germany.
Institute for Complex Systems and Mathematical Biology, University of Aberdeen, Aberdeen AB243UE, United Kingdom.
Department of Control Theory, Nizhny Novgorod State University, Gagarin Avenue 23, 606950 Nizhny Novgorod, Russia.


Long-range correlated processes are ubiquitous, ranging from climate variables to financial time series. One paradigmatic example for such processes is fractional Brownian motion (fBm). In this work, we highlight the potentials and conceptual as well as practical limitations when applying the recently proposed recurrence network (RN) approach to fBm and related stochastic processes. In particular, we demonstrate that the results of a previous application of RN analysis to fBm [Liu et al. Phys. Rev. E 89, 032814 (2014)] are mainly due to an inappropriate treatment disregarding the intrinsic nonstationarity of such processes. Complementarily, we analyze some RN properties of the closely related stationary fractional Gaussian noise (fGn) processes and find that the resulting network properties are well-defined and behave as one would expect from basic conceptual considerations. Our results demonstrate that RN analysis can indeed provide meaningful results for stationary stochastic processes, given a proper selection of its intrinsic methodological parameters, whereas it is prone to fail to uniquely retrieve RN properties for nonstationary stochastic processes like fBm.

[Indexed for MEDLINE]

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