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Related Experiment Video

Updated: Jun 12, 2026

Application of Granger Causality Analysis of the Directed Functional Connection in Alzheimer's Disease and Mild Cognitive Impairment

Application of Granger Causality Analysis of the Directed Functional Connection in Alzheimer's Disease and Mild Cognitive Impairment

Published on: August 7, 2017

Multivariate Granger causality and generalized variance.

Adam B Barrett¹, Lionel Barnett, Anil K Seth

¹Sackler Centre for Consciousness Science, School of Informatics, University of Sussex, Brighton BN1 9QJ, United Kingdom. adam.barrett@sussex.ac.uk

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|May 21, 2010

Summary

This summary is machine-generated.

This study extends Granger causality to analyze interactions among groups of variables, not just single ones. The new framework uses generalized variances for more comprehensive causal inference in complex systems.

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Decomposing the Variance in Reading Comprehension to Reveal the Unique and Common Effects of Language and Decoding

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Published on: October 11, 2018

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Last Updated: Jun 12, 2026

Application of Granger Causality Analysis of the Directed Functional Connection in Alzheimer's Disease and Mild Cognitive Impairment

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Published on: August 7, 2017

Decomposing the Variance in Reading Comprehension to Reveal the Unique and Common Effects of Language and Decoding

Decomposing the Variance in Reading Comprehension to Reveal the Unique and Common Effects of Language and Decoding

Published on: October 11, 2018

Area of Science:

Complex Systems Analysis
Statistical Inference
Neuroscience

Background:

Granger causality is standard for directed interactions in complex systems.
Current methods analyze only univariate (single) variable interactions.
Interactions can occur among groups (ensembles) of variables.

Purpose of the Study:

Establish a principled framework for multivariate Granger causality.
Extend Granger causality to analyze interactions among sets of variables.
Provide a theoretically consistent extension of Granger causality.

Main Methods:

Building on Geweke's (1982) work.
Utilizing generalized variances of residual errors.
Developing a framework for multivariate Granger causality.

Main Results:

A comprehensive and theoretically consistent extension of Granger causality to the multivariate case.
Specific advantages of the generalized variance measure highlighted.
Demonstrated applications in neuroscience.

Conclusions:

The generalized variance measure offers advantages for multivariate Granger causality.
The framework allows definition of partial Granger causality, causal density, and Granger autonomy.
Results are applicable to experimental data for revealing new functional relations in complex systems.