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

TL;DR

This paper evaluates the effectiveness of recurrence network analysis for long-term correlated stochastic processes, emphasizing its success for stationary processes like fractional Gaussian noise and limitations for non-stationary ones like fractional Brownian motion.

Contribution

It clarifies the potentials and pitfalls of recurrence network analysis for different types of long-range correlated processes, highlighting the importance of stationarity considerations.

Findings

RN analysis yields meaningful results for stationary processes like fGn.

RN analysis can fail for non-stationary processes like fBm if not properly applied.

Previous applications of RN to fBm overlooked non-stationarity issues.

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 \textit{et al.,} Phys. Rev. E \textbf{89}, 032814 (2014)) are mainly due to an inappropriate treatment disregarding the intrinsic non-stationarity 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 non-stationary stochastic processes like fBm.