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Using missing ordinal patterns to detect nonlinearity in time series data.

Christopher W Kulp1, Luciano Zunino2, Thomas Osborne1

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The number of missing ordinal patterns (NMP) effectively detects nonlinearity in time series data. This method proves reliable even for short datasets, offering a robust statistical test for complex systems.

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Area of Science:

  • Dynamical Systems and Chaos Theory
  • Time Series Analysis
  • Nonlinear Dynamics

Background:

  • Ordinal patterns provide insights into time series complexity.
  • The Bandt and Pompe methodology offers a framework for symbolizing time series.
  • Identifying nonlinearity is crucial for understanding complex systems.

Purpose of the Study:

  • To evaluate the number of missing ordinal patterns (NMP) as a statistical test for nonlinearity.
  • To assess the efficacy of NMP using a surrogate framework with IAAFT surrogates.
  • To determine if NMP is effective for short time series analysis.

Main Methods:

  • Symbolization of time series using the Bandt and Pompe method.
  • Calculation of the number of missing ordinal patterns (NMP).
  • Comparison of NMP values from original time series against IAAFT surrogates within a statistical framework.

Main Results:

  • The NMP was found to be a statistically significant indicator of nonlinearity.
  • The NMP test demonstrated effectiveness even with very short time series.
  • Both model and experimental data confirmed the efficacy of NMP.

Conclusions:

  • The number of missing ordinal patterns (NMP) serves as a reliable test statistic for nonlinearity.
  • NMP is a valuable tool for analyzing nonlinear dynamics in time series, particularly short ones.
  • The surrogate framework validates NMP's performance in detecting nonlinear characteristics.