@article {Wahl1314_2016,
	year = {2016},
	author = {Wahl, Benjamin and Feudel, Ulrike and Hlinka, Jaroslav and Wächter, Matthias and Peinke, Joachim and Freund, Jan A},
	title = {Granger-causality maps of diffusion processes},
	journal = {Physical review. E},
	volume = {93},
	number = {2},
	page = {022213},
	DOI = {10.1103/physreve.93.022213},
	ISSN = {2},
	abstract = {Granger causality is a statistical concept devised to reconstruct and quantify predictive information flow between stochastic processes. Although the general concept can be formulated model-free it is often considered in the framework of linear stochastic processes. Here we show how local linear model descriptions can be employed to extend Granger causality into the realm of nonlinear systems. This novel treatment results in maps that resolve Granger causality in regions of state space. Through examples we provide a proof of concept and illustrate the utility of these maps. Moreover, by integration we convert the local Granger causality into a global measure that yields a consistent picture for a global Ornstein-Uhlenbeck process. Finally, we recover invariance transformations known from the theory of autoregressive processes}
}