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Multivariate Granger causality and generalized variance

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posted on 2023-06-07, 23:35 authored by Adam BarrettAdam Barrett, Lionel BarnettLionel Barnett, Anil SethAnil Seth
Granger causality analysis is a popular method for inference on directed interactions in complex systems of many variables. A shortcoming of the standard framework for Granger causality is that it only allows for examination of interactions between single (univariate) variables within a system, perhaps conditioned on other variables. However, interactions do not necessarily take place between single variables but may occur among groups or "ensembles" of variables. In this study we establish a principled framework for Granger causality in the context of causal interactions among two or more multivariate sets of variables. Building on Geweke's seminal 1982 work, we offer additional justifications for one particular form of multivariate Granger causality based on the generalized variances of residual errors. Taken together, our results support a comprehensive and theoretically consistent extension of Granger causality to the multivariate case. Treated individually, they highlight several specific advantages of the generalized variance measure, which we illustrate using applications in neuroscience as an example. We further show how the measure can be used to define "partial" Granger causality in the multivariate context and we also motivate reformulations of "causal density" and "Granger autonomy." Our results are directly applicable to experimental data and promise to reveal new types of functional relations in complex systems, neural and otherwise.

History

Publication status

  • Published

File Version

  • Published version

Journal

Physical Review E

ISSN

1539-3755

Publisher

American Physical Society

Issue

4

Volume

81

Page range

041907

Department affiliated with

  • Informatics Publications

Full text available

  • Yes

Peer reviewed?

  • Yes

Legacy Posted Date

2012-02-06

First Open Access (FOA) Date

2015-06-25

First Compliant Deposit (FCD) Date

2015-06-25

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