Ordinal spectrum: a frequency domain characterization of complex time series

TL;DR

The paper introduces the ordinal spectrum, a novel frequency domain method based on symbolic sequences, to characterize the complexity of time series and distinguish chaotic dynamics from linear systems.

Contribution

It proposes the ordinal spectrum, a new spectral transformation technique that effectively captures nonlinear and chaotic behaviors in time series data.

Findings

Successfully distinguishes chaotic from linear systems

Provides new insights into nonlinear oscillations in real data

Effective on synthetic and real-world datasets

Abstract

Although classical spectral analysis is a natural approach to characterise linear systems, it cannot describe a chaotic dynamics. Here, we propose the ordinal spectrum, a method based on a spectral transformation of symbolic sequences, to characterise the complexity of a time series. In contrasts with other nonlinear mapping functions (e.g. the state-space reconstruction) the proposed representation is a natural approach to distinguish, in a frequency domain, a chaotic behavior. We test the method in different synthetic and real-world data. Our results suggest that the proposed approach may provide new insights into the non-linear oscillations observed in different real data.