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

Yong Zou*, Reik V. Donner, Juergen Kurths

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

13 Citations (Scopus)
21 Downloads (Pure)


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.

Original languageEnglish
Article number022926
Number of pages8
JournalPhysical Review. E, Statistical, Nonlinear and Soft Matter Physics
Issue number2
Publication statusPublished - 27 Feb 2015


  • detrended fluctuation analysis
  • time-series
  • strange attractors
  • systems
  • transitions
  • persistence
  • dimension
  • evolution
  • plots


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