Graphs for Dependence and Causality in Multivariate Time Series

  • Christoph Flamm
  • Ulrike Kalliauer
  • Manfred Deistler
  • Markus Waser
  • Andreas Graef


In this contribution we describe measures for dependence and causality between component processes in multivariate time series in a stationary context. Symmetric measures, such as the partial spectral coherence, as well as directed measures, such as the partial directed coherence and the conditional Granger causality index, are described and discussed. These measures are used for deriving undirected and directed graphs (where the vertices correspond to the one-dimensional component processes), showing the inner structure of a multivariate time series. Our interest in these graphs originates from the problem of detecting the focus of an epileptic seizure, based on the analysis of invasive EEG data. An example for such an analysis is given in the last section of this chapter.


Epileptic Seizure Granger Causality Epileptic Activity Multivariate Time Series Mixed Graph 
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Copyright information

© Springer-Verlag London Limited 2012

Authors and Affiliations

  • Christoph Flamm
    • 1
  • Ulrike Kalliauer
    • 2
  • Manfred Deistler
    • 1
  • Markus Waser
    • 1
  • Andreas Graef
    • 1
  1. 1.Institute for Mathematical Methods in EconomicsVienna University of TechnologyViennaAustria
  2. 2.VERBUND Trading AGViennaAustria

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