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Connectivity Inference between Neural Structures via Partial Directed Coherence

Author

Listed:
  • Daniel Yasumasa Takahashi
  • Luiz Antonio Baccal
  • Koichi Sameshima

Abstract

This paper describes the rigorous asymptotic distributions of the recently introduced partial directed coherence (PDC) - a frequency domain description of Granger causality between multivariate time series represented by vector autoregressive models. We show that, when not zero, PDC is asymptotically normally distributed and therefore provides means of comparing different strengths of connection between observed time series. Zero PDC indicates an absence of a direct connection between time series, and its otherwise asymptotically normal behavior degenerates into that of a mixture of [image omitted] variables allowing the computation of rigorous thresholds for connectivity tests using either numerical integration or approximate numerical methods. A Monte Carlo study illustrates the power of the test under PDC nullity. An analysis of electroencephalographic data, before and during an epileptic seizure episode, is used to portray the usefulness of the test in a real application.

Suggested Citation

  • Daniel Yasumasa Takahashi & Luiz Antonio Baccal & Koichi Sameshima, 2007. "Connectivity Inference between Neural Structures via Partial Directed Coherence," Journal of Applied Statistics, Taylor & Francis Journals, vol. 34(10), pages 1259-1273.
    • Handle: RePEc:taf:japsta:v:34:y:2007:i:10:p:1259-1273
    DOI: 10.1080/02664760701593065
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    Cited by:

    1. Zouhaier Dhifaoui & Sami Ben Jabeur & Rabeh Khalfaoui & Muhammad Ali Nasir, 2023. "Time‐varying partial‐directed coherence approach to forecast global energy prices with stochastic volatility model," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 42(8), pages 2292-2306, December.
    2. Alberto Porta & Luca Faes & Vlasta Bari & Andrea Marchi & Tito Bassani & Giandomenico Nollo & Natália Maria Perseguini & Juliana Milan & Vinícius Minatel & Audrey Borghi-Silva & Anielle C M Takahashi , 2014. "Effect of Age on Complexity and Causality of the Cardiovascular Control: Comparison between Model-Based and Model-Free Approaches," PLOS ONE, Public Library of Science, vol. 9(2), pages 1-14, February.
    3. Abdelwahab Allali & Amor Oueslati & Abdelwahed Trabelsi, 2011. "Detection of Information Flow in Major International Financial Markets by Interactivity Network Analysis," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 18(3), pages 319-344, September.
    4. Angeliki Papana & Catherine Kyrtsou & Dimitris Kugiumtzis & Cees Diks, 2017. "Assessment of resampling methods for causality testing: A note on the US inflation behavior," PLOS ONE, Public Library of Science, vol. 12(7), pages 1-20, July.

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