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Granger-causality maps of diffusion processes.

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Summary
This summary is machine-generated.

This study extends Granger causality to nonlinear systems using local linear models, creating state-space maps of information flow. This approach provides both local and global causality measures for complex stochastic processes.

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Area of Science:

  • Nonlinear dynamics
  • Statistical inference
  • Information theory

Background:

  • Granger causality quantifies predictive information flow between stochastic processes.
  • Traditional Granger causality is often limited to linear systems.
  • Extending causality measures to nonlinear systems is a significant challenge.

Purpose of the Study:

  • To develop a method for extending Granger causality to nonlinear systems.
  • To create state-space maps that visualize Granger causality in localized regions.
  • To establish a global measure of Granger causality through integration.

Main Methods:

  • Employing local linear model descriptions to approximate nonlinear systems.
  • Developing state-space mapping techniques for Granger causality.
  • Integrating local causality measures to derive a global metric.

Main Results:

  • Novel treatment extends Granger causality to nonlinear systems.
  • State-space maps effectively resolve Granger causality in specific regions.
  • A global measure of Granger causality is derived and validated for Ornstein-Uhlenbeck processes.
  • Invariance transformations from autoregressive processes are recovered.

Conclusions:

  • Local linear models provide a powerful framework for nonlinear Granger causality.
  • State-space maps offer detailed insights into information flow in complex systems.
  • The developed methods yield consistent global causality measures and recover known theoretical properties.