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Linear and nonlinear causality between signals: methods, examples and neurophysiological applications. (English) Zbl 1161.62429
Summary: We present and review the most usual methods to detect linear and nonlinear causality between signals: the linear Granger causality test extended to direct causality in the multivariate case (LGC), directed coherence, partial directed coherence (PDC), and the nonlinear Granger causality test extended to direct causality in the 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. The PNGC is extremely dependent on the choice of the 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.

MSC:
62P10 Applications of statistics to biology and medical sciences; meta analysis
92C20 Neural biology
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