Assessing Nonlinear Granger Causality from Multivariate Time Series

  • Xiaohai Sun
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5212)


A straightforward nonlinear extension of Granger’s concept of causality in the kernel framework is suggested. The kernel-based approach to assessing nonlinear Granger causality in multivariate time series enables us to determine, in a model-free way, whether the causal relation between two time series is present or not and whether it is direct or mediated by other processes. The trace norm of the so-called covariance operator in feature space is used to measure the prediction error. Relying on this measure, we test the improvement of predictability between time series by subsampling-based multiple testing. The distributional properties of the resulting p-values reveal the direction of Granger causality. Experiments with simulated and real-world data show that our method provides encouraging results.


time series Granger causality kernel methods 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Xiaohai Sun
    • 1
  1. 1.Max Planck Institute for Biological Cybernetics TübingenGermany

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