Kernel method for nonlinear Granger causality

Abstract

Important information on the structure of complex systems, consisting of more than one component, can be obtained by measuring to which extent the individual components exchange information among each other. Such knowledge is needed to reach a deeper comprehension of phenomena ranging from turbulent fluids to neural networks, as well as complex physiological signals. 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.

Revised version, accepted for publication on Physical Review Letters

References in corpus (8)

• Measuring Information Transfer
• On the performance of different synchronization measures in real data: a case study on EEG signals
• Analyzing Multiple Nonlinear Time Series with Extended Granger Causality
• Estimating Granger causality from Fourier and wavelet transforms of time series data
• Quantifying Self-Organization with Optimal Predictors
• Mitigating the effects of measurement noise on Granger causality
• Nonlinear parametric model for Granger causality of time series
• Granger Causality and Cross Recurrence Plots in Rheochaos

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