Correntropy-based partial directed coherence for testing multivariate Granger causality in nonlinear processes.

Area of Science:

• * Multivariate Systems Analysis
• * Nonlinear Dynamics
• * Information Theory

Background:

• * Identifying directional influences is crucial in fields like engineering and neurosciences.
• * Existing methods like Partial Directed Coherence (PDC) are linear and limited, while Transfer Entropy is computationally intensive and restricted to bivariate systems.
• * A need exists for a nonlinear directionality measure that is both simple and broadly applicable.

Purpose of the Study:

• * To develop a nonlinear directionality measure, Kernel Partial Directed Coherence (KPDC).
• * To achieve the simplicity of PDC while extending applicability to nonlinear processes.
• * To provide a robust tool for analyzing complex systems with nonlinear interactions.

Main Methods:

• * The Kernel Partial Directed Coherence (KPDC) method is founded on correntropy, a generalized correlation measure.
• * KPDC constructs a vector autoregressive model in a kernel space based on correntropy.
• * A consistent estimator for KPDC is developed, alongside a permutation scheme and sequential Bonferroni procedure for hypothesis testing.

Main Results:

• * Theoretical results establishing the properties of the KPDC estimator are derived.
• * The proposed permutation scheme effectively tests for the absence of Granger causality.
• * Case studies demonstrate the methodology's ability to detect Granger causality in nonlinear processes.

Conclusions:

• * KPDC successfully addresses the limitations of existing linear and nonlinear directionality measures.
• * The method provides a computationally feasible and effective approach for nonlinear system analysis.
• * KPDC enhances the understanding of directional influences in complex multivariate systems.