Inference of Granger causal time-dependent influences in noisy multivariate time series

Linda Sommerlade, Marco Thiel, Bettina Platt, Andrea Plano, Gernot Riedel, Celso Grebogi, Jens Timmer, Bjoern Olaf Schelter

Research output: Contribution to journalArticlepeer-review

44 Citations (Scopus)


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. (C) 2011 Elsevier B.V. All rights reserved.

Original languageEnglish
Pages (from-to)173-185
Number of pages13
JournalJournal of Neuroscience Methods
Issue number1
Early online date16 Sept 2011
Publication statusPublished - 15 Jan 2012


  • non-stationary causal influences
  • time-resolved partial directed coherence
  • vector autoregressive processes
  • state space models
  • expectation-maximization algorithm
  • partial directed coherence
  • functional connectivity
  • maximum-likelihood
  • information-flow
  • signals
  • sleep
  • EEG
  • algorithm
  • behavior
  • systems


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