A highly specific test for periodicity

TL;DR

This paper introduces a conservative, parameter-free method for distinguishing nearly periodic from strictly periodic time series, especially useful for analyzing deterministic dynamical systems, outperforming marker-based approaches in detecting small deviations.

Contribution

The paper presents a novel, highly specific periodicity test that requires no parameter tuning and provides precise period length estimation, improving over existing marker-event methods.

Findings

Effective in detecting small deviations from periodicity

Outperforms marker-event-based approaches in typical scenarios

Requires no parameter adjustment and has linear runtime growth

Abstract

We present a method that allows to distinguish between nearly periodic and strictly periodic time series. To this purpose, we employ a conservative criterion for periodicity, namely that the time series can be interpolated by a periodic function whose local extrema are also present in the time series. Our method is intended for the analysis of time series generated by deterministic time-continuous dynamical systems, where it can help telling periodic dynamics from chaotic or transient ones. We empirically investigate our method's performance and compare it to an approach based on marker events (or Poincar\'e sections). We demonstrate that our method is capable of detecting small deviations from periodicity and outperforms the marker-event-based approach in typical situations. Our method requires no adjustment of parameters to the individual time series, yields the period length with a precision that exceeds the sampling rate, and its runtime grows asymptotically linear with the length of the time series.