2019/10/03 by Arthur A. B. Pessa, Haroldo V. Ribeiro · 1 citation
Computer Science · Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #Algorithm #Brownian motion #Chaos control and synchronization #Complex Systems and Time Series Analysis #Complex network #Computer science #Entropy (arrow of time) #Fractional Brownian motion #Hurst exponent #Mathematics #Ordinal data #Ordinal regression #Series (stratigraphy) #Statistical physics #Statistics #Time Series Analysis and Forecasting #Time series #physics.data-an
paper · pdf · doi:10.1103/physreve.100.042304
published as Phys. Rev. E 100, 042304 (2019) · 14 two-column pages, 8 figures; accepted for publication in Physical Review E
arxiv created 2019/10/03 · openalex publication_date 2019/10/14 · arxiv updated 2019/10/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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 their 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 nonrandom 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's seismic activity caused by large earthquakes.