Quantifying the irregularity of a time series

TL;DR

This paper introduces circulance, a scalar measure derived from directed ordinal pattern networks, to quantify the degree of regularity or irregularity in time series from dynamical systems, aiding in regime classification.

Contribution

The paper presents circulance as a novel, robust metric for classifying time series based on their dynamical regimes, applicable to both model systems and empirical data.

Findings

Circulance effectively distinguishes between different dynamical regimes.

It robustly positions time series along a spectrum from regularity to randomness.

Application to real-world data from the human brain and the Sun demonstrates its practical utility.

Abstract

We introduce circulance, a scalar measure for classifying time series of dynamical systems. Circulance captures the extent of temporal regularity or irregularity that is encoded in the topology of a directed ordinal pattern transition network derived from a time series. We demonstrate numerically that circulance sensitively and robustly positions time series of canonical model systems, representative of preset dynamical regimes, along a continuous spectrum from regularity to randomness. Analyzing empirical data from long-term observations of high-dimensional, complex systems -- human brain and the Sun -- reveals that circulance aids in elucidating different dynamical regimes.