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Detecting directional couplings from multivariate flows by the joint distance distribution.

José M Amigó1, Yoshito Hirata2

  • 1Centro de Investigación Operativa, Universidad Miguel Hernández, Avda. de la Universidad s/n, 03202 Elche, Spain.

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This study introduces a new method, the joint distance distribution, to identify cause-effect relationships in nonlinear systems using only observational data. The method shows promise, outperforming transfer entropy in certain scenarios.

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Area of Science:

  • Nonlinear Dynamics
  • Complex Systems Analysis
  • Causality Inference

Background:

  • Understanding directional couplings in interacting nonlinear systems is crucial for analyzing their dynamics.
  • Causality detection from time series data is challenging, especially with limited prior knowledge.
  • Existing methods like Granger causality and transfer entropy have limitations and ongoing research areas.

Purpose of the Study:

  • To re-examine and apply the joint distance distribution method for detecting directional couplings in multivariate time series.
  • To assess the effectiveness of this method, particularly when dealing with complex interaction networks and hidden common drivers.
  • To compare the performance of the joint distance distribution against transfer entropy.

Main Methods:

  • Utilizing the joint distance distribution method, based on the forced Takens theorem.
  • Exploiting continuous mappings between reconstructed attractors of driving and response systems.
  • Applying the method to Lorenz and Rössler oscillators in various interaction network configurations.

Main Results:

  • The joint distance distribution method yielded satisfactory results for Lorenz and Rössler oscillators, even with hidden common drivers.
  • The method demonstrated superior performance compared to the lowest dimensional transfer entropy in the considered cases.
  • Robustness analysis confirmed the method's reliability concerning sampling interval, time series length, noise, and metric.

Conclusions:

  • The joint distance distribution is a viable and effective tool for identifying directional couplings in nonlinear systems from observational data.
  • This method offers an advantage over transfer entropy in specific complex system analyses.
  • Further research into causality detection methods is active, with this approach showing significant potential.