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A robust time-delay selection criterion applied to convergent cross mapping.

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This study introduces a new method for selecting time delays in dynamical systems by optimizing mutual information. This approach is more reliable than existing methods, especially with noisy data, improving causality detection.

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Area of Science:

  • Dynamical systems theory
  • Nonlinear dynamics
  • Information theory

Background:

  • Selecting an appropriate time delay is crucial for accurately embedding dynamical systems.
  • Existing methods often rely on local minima of mutual information, which can be unreliable in noisy conditions.
  • Robust time delay selection is essential for reliable causality detection.

Purpose of the Study:

  • To present a novel heuristic for time delay selection in dynamical systems.
  • To optimize the global maximum of mutual information in orthonormal coordinates.
  • To demonstrate the robustness and improved performance compared to local minimum methods.

Main Methods:

  • Utilizing a heuristic based on optimizing the global maximum of mutual information.
  • Employing orthonormal coordinates for system embedding.
  • Comparing performance with local minimum methods using convergent cross mapping.
  • Testing with a noisy Lorenz system and experimental plasma data.

Main Results:

  • The global maximum method is more robust than local minimum methods, especially in the presence of noise.
  • The proposed heuristic guarantees the existence of a global maximum in the chosen coordinate system.
  • The method shows improved consistency and accuracy in time lag selection for causality detection.
  • Experimental data from an oscillating plasma source validates the findings.

Conclusions:

  • The heuristic optimizing the global maximum of mutual information offers a more reliable approach to time delay selection.
  • This method enhances the accuracy of causality detection in dynamical systems, particularly under noisy conditions.
  • The findings suggest a significant advancement in time series analysis for complex systems.