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 journalArticle

9 Citations (Scopus)
21 Downloads (Pure)

Abstract

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
Volume91
Issue number2
DOIs
Publication statusPublished - 27 Feb 2015

Fingerprint

stochastic processes
Recurrence
Stochastic Processes
Fractional Brownian Motion
network analysis
Network Analysis
Fractional Gaussian Noise
random noise
Nonstationary Processes
Nonstationarity
Financial Time Series
climate
Stationary Process
Climate
Demonstrate
Well-defined
Range of data

Keywords

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

Cite this

Analyzing long-term correlated stochastic processes by means of recurrence networks : Potentials and pitfalls. / Zou, Yong; Donner, Reik V.; Kurths, Juergen.

In: Physical Review. E, Statistical, Nonlinear and Soft Matter Physics, Vol. 91, No. 2, 022926, 27.02.2015.

Research output: Contribution to journalArticle

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N1 - ACKNOWLEDGMENTS Y.Z. acknowledges financial support by the NNSF of China (Grants No. 11305062, No. 11135001, and No. 81471651), the Specialized Research Fund (SRF) for the Doctoral Program (Grant No. 20130076120003), the SRF for ROCS, SEM, the Open Project Program of State Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, China (Grant No.Y4KF151CJ1), and the German Academic Exchange Service (DAAD). R.V.D. has been funded by the German Federal Ministry for Education and Research (BMBF) via the Young Investigator’s group CoSy-CC2 (Project No. 01LN1306A). The authors thank the anonymous reviewers for helpful remarks on the original version of this manuscript.

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