Kernel Method for Nonlinear Granger Causality

2007/11/30 by Daniele Marinazzo, Mario Pellicoro, M. Pellicoro +1 · 411 citations
Computer Science · Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #Algorithm #Applied mathematics #Artificial intelligence #Artificial neural network #Causality (physics) #Chaos control and synchronization #Chaotic #Complex Systems and Time Series Analysis #Computer science #Discrete mathematics #Feature (linguistics) #Granger causality #Hilbert space #Kernel (algebra) #Kernel method #Machine learning #Mathematical analysis #Mathematics #Neural Networks and Applications #Nonlinear system #Overfitting #Physics #Reproducing kernel Hilbert space #Series (stratigraphy) #Support vector machine #cond-mat.dis-nn #nlin.SI

paper · pdf · doi:10.1103/physrevlett.100.144103

published in Physical Review Letters 100(14), 144103 (American Physical Society) · Revised version, accepted for publication on Physical Review Letters

arxiv created 2008/03/20 · openalex publication_date 2008/04/11 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

Important information on the structure of complex systems can be obtained by measuring to what extent the individual components exchange information among each other. The linear Granger approach, to detect cause-effect relationships between time series, has emerged in recent years as a leading statistical technique to accomplish this task. Here we generalize Granger causality to the nonlinear case using the theory of reproducing kernel Hilbert spaces. Our method performs linear Granger causality in the feature space of suitable kernel functions, assuming arbitrary degree of nonlinearity. We develop a new strategy to cope with the problem of overfitting, based on the geometry of reproducing kernel Hilbert spaces. Applications to coupled chaotic maps and physiological data sets are presented.

Citations

• Investigating Causal Relations by Econometric Models and Cross-spectral Methods

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