Characterizing stochastic time series with ordinal networks

TL;DR

This paper explores the properties of ordinal networks derived from various stochastic and real-world time series, demonstrating their effectiveness in detecting non-random behavior, estimating the Hurst exponent, and identifying seismic activity changes.

Contribution

It extends the application of ordinal networks to stochastic processes and real-world data, providing new methods for analyzing randomness, noise robustness, and seismic event detection.

Findings

Ordinal networks can accurately detect non-random behavior.

Average local entropy is more noise-robust than permutation entropy.

Ordinal networks effectively estimate the Hurst exponent and detect seismic activity changes.

Abstract

Approaches for mapping time series to networks have become essential tools for dealing with the increasing challenges of characterizing data from complex systems. Among the different algorithms, the recently proposed ordinal networks stand out due to its simplicity and computational efficiency. However, applications of ordinal networks have been mainly focused on time series arising from nonlinear dynamical systems, while basic properties of ordinal networks related to simple stochastic processes remain poorly understood. Here, we investigate several properties of ordinal networks emerging from random time series, noisy periodic signals, fractional Brownian motion, and earthquake magnitude series. For ordinal networks of random series, we present an approach for building the exact form of the adjacency matrix, which in turn is useful for detecting non-random behavior in time series and the existence of missing transitions among ordinal patterns. We find that the average value of a local entropy, estimated from transition probabilities among neighboring nodes of ordinal networks, is more robust against noise addition than the standard permutation entropy. We show that ordinal networks can be used for estimating the Hurst exponent of time series with accuracy comparable with state-of-the-art methods. Finally, we argue that ordinal networks can detect sudden changes in Earth seismic activity caused by large earthquakes.