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Evaluating Temporal Correlations in Time Series Using Permutation Entropy, Ordinal Probabilities and Machine

Bruno R R Boaretto1, Roberto C Budzinski2,3, Kalel L Rossi4

  • 1Department of Physics, Universidade Federal do Paraná, Curitiba 81531-980, Brazil.

Entropy (Basel, Switzerland)
|August 27, 2021
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Summary
This summary is machine-generated.

This study introduces a novel machine learning method to quantify nonlinear temporal correlations in time series data. The approach accurately estimates correlation parameters and identifies underlying determinism, offering new insights into complex systems.

Keywords:
chaoscomplexitymachine learningnoiseordinal analysispermutation entropysymbolic analysistime series analysis

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Area of Science:

  • Complex Systems Analysis
  • Nonlinear Dynamics
  • Machine Learning Applications

Background:

  • Time series analysis faces challenges in quantifying nonlinear temporal correlations.
  • Existing methods may not fully capture the complexity of temporal dependencies.

Purpose of the Study:

  • To introduce and validate a new machine learning-based methodology for analyzing nonlinear temporal correlations.
  • To quantify the strength of temporal correlations and identify determinism in time series data.
  • To assess the correlation of new quantifiers with established chaos and complexity measures.

Main Methods:

  • Training a machine learning algorithm using ordinal pattern probabilities from flicker noise (FN) time series.
  • Predicting the temporal correlation parameter (α) of FN time series.
  • Utilizing the difference in permutation entropy (PE) between a time series and a generated FN time series to identify determinism (Ω).

Main Results:

  • The developed algorithm successfully estimates the temporal correlation parameter (αe) from time series.
  • The Ω quantifier effectively aids in identifying underlying determinism.
  • Analysis shows correlations between αe, Ω, and established quantifiers of chaos and complexity.

Conclusions:

  • The proposed methodology offers a robust approach to quantifying nonlinear temporal correlations and determinism.
  • The method demonstrates utility across diverse datasets, correlating well with existing complexity measures.
  • Limitations in highly chaotic and noisy periodic time series are acknowledged, with open-source code provided.