title: Inference of Granger causal time-dependent influences in noisy multivariate time series.
abstract: Inferring Granger-causal interactions between processes promises deeper insights into mechanisms underlying network phenomena, e.g. in the neurosciences where the level of connectivity in neural networks is of particular interest. Renormalized partial directed coherence has been introduced as a means to investigate Granger causality in such multivariate systems. A major challenge in estimating respective coherences is a reliable parameter estimation of vector autoregressive processes. We discuss two shortcomings typical in relevant applications, i.e. non-stationarity of the processes generating the time series and contamination with observational noise. To overcome both, we present a new approach by combining renormalized partial directed coherence with state space modeling. A numerical efficient way to perform both the estimation as well as the statistical inference will be presented.
authors.affiliation: Department of Physics, University of Freiburg, Hermann-Herder-Str. 3, 79104 Freiburg, Germany. linda.sommerlade@fdm.uni-freiburg.de
authors.forename: Linda
authors.initials: L
authors.lastname: Sommerlade
authors.forename: Marco
authors.initials: M
authors.lastname: Thiel
authors.forename: Bettina
authors.initials: B
authors.lastname: Platt
authors.forename: Andrea
authors.initials: A
authors.lastname: Plano
authors.forename: Gernot
authors.initials: G
authors.lastname: Riedel
authors.forename: Celso
authors.initials: C
authors.lastname: Grebogi
authors.forename: Jens
authors.initials: J
authors.lastname: Timmer
authors.forename: Björn
authors.initials: B
authors.lastname: Schelter
mesh_terms: D000465:Algorithms; D000818:Animals; D001921:Brain / Q000502:physiology*; D003198:Computer Simulation; D004569:Electroencephalography; D051379:Mice; D008959:Models, Neurological; D008962:Models, Theoretical; D009415:Nerve Net / Q000502:physiology*