PhysRevE.81.041907.pdf (246.7 kB)
Multivariate Granger causality and generalized variance
journal contribution
posted on 2023-06-07, 23:35 authored by Adam BarrettAdam Barrett, Lionel BarnettLionel Barnett, Anil SethAnil SethGranger 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.
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Publication status
- Published
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- Published version
Journal
Physical Review EISSN
1539-3755Publisher
American Physical SocietyExternal DOI
Issue
4Volume
81Page range
041907Department affiliated with
- Informatics Publications
Full text available
- Yes
Peer reviewed?
- Yes
Legacy Posted Date
2012-02-06First Open Access (FOA) Date
2015-06-25First Compliant Deposit (FCD) Date
2015-06-25Usage metrics
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