Biological Cybernetics

, Volume 95, Issue 4, pp 349–369 | Cite as

Linear and nonlinear causality between signals: methods, examples and neurophysiological applications

  • Boris GourévitchEmail author
  • Régine Le Bouquin-Jeannès
  • Gérard Faucon
Original Paper


In this paper, we will present and review the most usual methods to detect linear and nonlinear causality between signals: linear Granger causality test (Geweke in J Am Stat Assoc 77:304–313, 1982) extended to direct causality in multivariate case (LGC), directed coherence (DCOH, Saito and Harashima in Recent advances in EEG and EMG data processing, Elsevier, Amsterdam, 1981), partial directed coherence (PDC, Sameshima and Baccala 1999) and nonlinear Granger causality test of Baek and Brock (in Working Paper University of Iowa, 1992) extended to direct causality in multivariate case (partial nonlinear Granger causality, PNGC). All these methods are tested and compared on several ARX, Poisson and nonlinear models, and on neurophysiological data (depth EEG). The results show that LGC, DCOH and PDC are not very robust in relation to nonlinear linkages but they seem to correctly find linear linkages if only the autoregressive parts are nonlinear. PNGC is extremely dependent on the choice of parameters. Moreover, LGC and PNGC may give misleading results in the case of causality on a spectral band, which is illustrated by our neurophysiological database.


Adjacency Matrix Granger Causality Planum Temporale Neurosci Method Directed Transfer Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Supplementary material

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Supplementary material


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Copyright information

© Springer-Verlag 2006

Authors and Affiliations

  • Boris Gourévitch
    • 1
    Email author
  • Régine Le Bouquin-Jeannès
    • 1
  • Gérard Faucon
    • 1
  1. 1.Laboratoire Traitement du Signal et de l’ImageInserm U642, Université de Rennes 1Rennes CedexFrance

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