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

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.