Detecting series periodicity with horizontal visibility graphs

TL;DR

This paper introduces a graph-based method using horizontal visibility graphs to detect hidden periodicity in noisy time series, offering an alternative to traditional autocorrelation techniques.

Contribution

It proposes a novel graph theoretical noise reduction filter and demonstrates its effectiveness in identifying periods in noisy signals.

Findings

The method accurately detects periods in noisy signals.

It outperforms standard autocorrelation methods in certain scenarios.

Potential applications include signal processing and time series analysis.

Abstract

The horizontal visibility algorithm has been recently introduced as a mapping between time series and networks. The challenge lies in characterizing the structure of time series (and the processes that generated those series) using the powerful tools of graph theory. Recent works have shown that the visibility graphs inherit several degrees of correlations from their associated series, and therefore such graph theoretical characterization is in principle possible. However, both the mathematical grounding of this promising theory and its applications are on its infancy. Following this line, here we address the question of detecting hidden periodicity in series polluted with a certain amount of noise. We first put forward some generic properties of horizontal visibility graphs which allow us to define a (graph theoretical) noise reduction filter. Accordingly, we evaluate its performance for the task of calculating the period of noisy periodic signals, and compare our results with standard time domain (autocorrelation) methods. Finally, potentials, limitations and applications are discussed.