# Nonlinear connectivity by Granger causality.

##### Citations

2,822 citations

### Cites background from "Nonlinear connectivity by Granger c..."

...Having said this, each clever refinement and generalization of Granger causality (e.g., Deshpande et al., 2010; Havlicek et al., 2010; Marinazzo et al., 2010) brings it one step closer to DCM (at least from my point of view)....

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385 citations

### Cites background from "Nonlinear connectivity by Granger c..."

..., 2005) GCM has also been extended to cover nonlinear stateequations (Freiwald et al., 1999; Marinazzo et al., 2011)....

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...There are a number of nonlinear WAGS methods that have been proposed for analyzing directed effective connectivity (Freiwald et al., 1999, Solo, 2008; Gourieroux et al., 1987; Marinazzo et al., 2011; Kalitzin et al., 2007) 3....

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342 citations

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##### References

26,531 citations

### "Nonlinear connectivity by Granger c..." refers methods in this paper

...Kernel algorithms work by embedding data into a Hilbert space, and searching for linear relations in that space (Vapnik, 1998) (for precise information on the geometry of least square regression and projection matrices, see Davidson and MacKinnon, 2004)....

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17,362 citations

16,349 citations

### "Nonlinear connectivity by Granger c..." refers background in this paper

...Granger causality analysis (Granger, 1969; Wiener, 1956) is an approach that measures the causal association and effective connectivity and can provide information about the dynamics and directionality on both electroencephalography (EEG) (Brovelli et al., 2004; Guo et al., 2008; Kaminski et al.,…...

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13,886 citations

### "Nonlinear connectivity by Granger c..." refers background or methods in this paper

...When choosing the kernel for the model, it is important that the model itself will be matched to the dynamical characteristics of the signal, as correctly pointed out in Pereda et al. (2005). In KGC, we deal with problem (i) performing a preliminary analysis in which we look how the causality indices change with the order p of the polynomial kernel, orwith theσ of theGaussian kernel, and theparameter is chosen according to the stability of the results....

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...the function which minimizes the risk functional (Papoulis 1985)) does not change when new variables, statistically independent of input and target variables, are added to the set of input variables....

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11,896 citations

### "Nonlinear connectivity by Granger c..." refers background in this paper

...Granger causality analysis (Granger, 1969; Wiener, 1956) is an approach that measures the causal association and effective connectivity and can provide information about the dynamics and directionality on both electroencephalography (EEG) (Brovelli et al., 2004; Guo et al., 2008; Kaminski et al.,…...

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...E-mail address: daniele.marinazzo@gmail.com (Dan 1053-8119/$ – see front matter © 2010 Elsevier Inc. Al doi:10.1016/j.neuroimage.2010.01.099 a b s t r a c t a r t i c l e i n f o...

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