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Long-range correlated processes are ubiquitous, ranging from climatevariables to financial time series. One paradigmatic example for such processesis fractional Brownian motion (fBm). In this work, we highlight the potentialsand conceptual as well as practical limitations when applying the recentlyproposed recurrence network (RN) approach to fBm and related stochasticprocesses. In particular, we demonstrate that the results of a previousapplication of RN analysis to fBm (Liu \textit{et al.,} Phys. Rev. E\textbf{89}, 032814 (2014)) are mainly due to an inappropriate treatmentdisregarding the intrinsic non-stationarity of such processes. Complementarily,we analyze some RN properties of the closely related stationary fractionalGaussian noise (fGn) processes and find that the resulting network propertiesare well-defined and behave as one would expect from basic conceptualconsiderations. Our results demonstrate that RN analysis can indeed providemeaningful results for stationary stochastic processes, given a properselection of its intrinsic methodological parameters, whereas it is prone tofail to uniquely retrieve RN properties for non-stationary stochastic processeslike fBm.

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