A procedure to increase the power of Granger-causal analysis through temporal smoothing

E. Spencer, L. E. Martinet, E. N. Eskandar, C. J. Chu, E. D. Kolaczyk, S. S. Cash, U. T. Eden, M. A. Kramer

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


Background: How the human brain coordinates network activity to support cognition and behavior remains poorly understood. New high-resolution recording modalities facilitate a more detailed understanding of the human brain network. Several approaches have been proposed to infer functional networks, indicating the transient coordination of activity between brain regions, from neural time series. One category of approach is based on statistical modeling of time series recorded from multiple sensors (e.g., multivariate Granger causality). However, fitting such models remains computationally challenging as the history structure may be long in neural activity, requiring many model parameters to fully capture the dynamics. New Method: We develop a method based on Granger causality that makes the assumption that the history dependence varies smoothly. We fit multivariate autoregressive models such that the coefficients of the lagged history terms are smooth functions. We do so by modelling the history terms with a lower dimensional spline basis, which requires many fewer parameters than the standard approach and increases the statistical power of the model. Results: We show that this procedure allows accurate estimation of brain dynamics and functional networks in simulations and examples of brain voltage activity recorded from a patient with pharmacoresistant epilepsy. Comparison with Existing Method: The proposed method has more statistical power than the Granger method for networks of signals that exhibit extended and smooth history dependencies. Conclusions: The proposed tool permits conditional inference of functional networks from many brain regions with extended history dependence, furthering the applicability of Granger causality to brain network science.

Original languageEnglish (US)
Pages (from-to)48-61
Number of pages14
JournalJournal of Neuroscience Methods
StatePublished - Oct 1 2018


  • Autoregressive modeling
  • Functional connectivity
  • Granger causality
  • Time series analysis

ASJC Scopus subject areas

  • General Neuroscience


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