title: Granger-causality maps of diffusion processes.
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.
authors.affiliation: Institute for Chemistry and Biology of the Marine Environment, University of Oldenburg, 26129 Oldenburg, Germany.|ForWind Center for Wind Energy Research, Institute of Physics, University of Oldenburg, 26129 Oldenburg, Germany.
authors.forename: Benjamin
authors.initials: B
authors.lastname: Wahl
authors.affiliation: Institute for Chemistry and Biology of the Marine Environment, University of Oldenburg, 26129 Oldenburg, Germany.
authors.forename: Ulrike
authors.initials: U
authors.lastname: Feudel
authors.affiliation: Institute of Computer Science, The Czech Academy of Sciences of the Czech Republic, 18207 Prague, Czech Republic.|National Institute of Mental Health, Klecany, Czech Republic.
authors.forename: Jaroslav
authors.initials: J
authors.lastname: Hlinka
authors.affiliation: ForWind Center for Wind Energy Research, Institute of Physics, University of Oldenburg, 26129 Oldenburg, Germany.
authors.forename: Matthias
authors.initials: M
authors.lastname: Wächter
authors.affiliation: ForWind Center for Wind Energy Research, Institute of Physics, University of Oldenburg, 26129 Oldenburg, Germany.
authors.forename: Joachim
authors.initials: J
authors.lastname: Peinke
authors.affiliation: Institute for Chemistry and Biology of the Marine Environment, University of Oldenburg, 26129 Oldenburg, Germany.
authors.forename: Jan A
authors.initials: JA
authors.lastname: Freund
mesh_terms: D004058:Diffusion; D016014:Linear Models; D008962:Models, Theoretical; D017711:Nonlinear Dynamics