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A highly specific test for periodicity.

Gerrit Ansmann1

  • 1Department of Epileptology, University of Bonn, Sigmund-Freud-Straße 25, 53105 Bonn, Germany; Helmholtz Institute for Radiation and Nuclear Physics, University of Bonn, Nussallee 14-16, 53115 Bonn, Germany; and Interdisciplinary Center for Complex Systems, University of Bonn, Brühler Straße 7, 53175 Bonn, Germany.

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This study introduces a novel method to differentiate between nearly periodic and strictly periodic time series using a conservative interpolation criterion. The approach accurately detects deviations from periodicity in dynamical systems, outperforming existing marker-event methods.

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Area of Science:

  • Dynamical Systems Analysis
  • Time Series Analysis
  • Nonlinear Dynamics

Background:

  • Distinguishing periodic from non-periodic dynamics is crucial in analyzing time series from deterministic systems.
  • Existing methods like Poincaré sections can be sensitive to parameter choices and may miss subtle deviations.

Purpose of the Study:

  • To develop a robust method for distinguishing nearly periodic from strictly periodic time series.
  • To provide a tool for identifying periodic dynamics in time-continuous deterministic systems.

Main Methods:

  • A conservative criterion for periodicity based on interpolation by a periodic function.
  • The method identifies local extrema of the time series within the interpolating function.
  • Empirical performance evaluation and comparison with marker-event approaches.

Main Results:

  • The proposed method accurately detects small deviations from periodicity.
  • It outperforms marker-event-based approaches in typical scenarios.
  • The method is parameter-free and provides period length with high precision.

Conclusions:

  • The new method offers a reliable way to classify time series periodicity.
  • It is particularly useful for analyzing time-continuous dynamical systems.
  • The approach is efficient with asymptotically linear runtime complexity.