Granger causality between vectors of time series: A puzzling property

Triacca, Umberto

doi:10.1016/j.spl.2018.06.009

Cited by 3 publications

(2 citation statements)

References 11 publications

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“…A recent study on the role of individual nodes in a complex network [ 22 ] may be viewed as another effort. (Causality analyses between subspaces with the classical approaches are rare; a few examples are [ 23 , 24 ], etc.) However, a rigorous formalism for more generic problems (e.g., with mutual causality involved) is yet to be implemented.…”

Section: Introductionmentioning

confidence: 99%

The Causal Interaction between Complex Subsystems

Liang

2021

Entropy

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Information flow provides a natural measure for the causal interaction between dynamical events. This study extends our previous rigorous formalism of componentwise information flow to the bulk information flow between two complex subsystems of a large-dimensional parental system. Analytical formulas have been obtained in a closed form. Under a Gaussian assumption, their maximum likelihood estimators have also been obtained. These formulas have been validated using different subsystems with preset relations, and they yield causalities just as expected. On the contrary, the commonly used proxies for the characterization of subsystems, such as averages and principal components, generally do not work correctly. This study can help diagnose the emergence of patterns in complex systems and is expected to have applications in many real world problems in different disciplines such as climate science, fluid dynamics, neuroscience, financial economics, etc.

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Section: Introductionmentioning

confidence: 99%

The Causal Interaction between Complex Subsystems

Liang

2021

Entropy

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“…The recent study on the role of individual nodes in a complex network, [22], may be viewed as another effort. (Causality analyses between subspaces with the classical approaches are rare; a few examples are [23], [24], etc.) But a rigorous formalism for more generic problems (e.g., with mutual causality involved) is yet to be implemented.…”

Section: Introductionmentioning

confidence: 99%

The causal interaction between the subnetworks of a complex network

Liang¹

2021

Preprint

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Information flow provides a natural measure for the causal interaction between dynamical events. This study extends our previous rigorous formalism of componentwise information flow to the bulk information flow between two complex subsystems of a large-dimensional parental system, in order to investigate problems such as the effective connectivity between two brain regions, each with millions of neurons involved. Analytical formulas have been obtained in a closed form. Under a Gaussian assumption, their maximum likelihood estimators have also been obtained. These formulas have been validated using different subsystems with preset relations, and they yield causalities just as expected. On the contrary, the commonly used proxies for the characterization of subsystems, such as averages and principal components, generally do not work correctly. This study can help diagnose the emergence of patterns in complex systems (e.g., the human brain), and is expected to have applications in many real world problems in different disciplines such as neuroscience, climate science, fluid dynamics, financial economics, to name a few.

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Nonlinear fault detection for batch processes via improved chordal kernel tensor locality preserving projections

Zhou

et al. 2020

Control Engineering Practice

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Granger causality between vectors of time series: A puzzling property

Cited by 3 publications

References 11 publications

The Causal Interaction between Complex Subsystems

The Causal Interaction between Complex Subsystems

The causal interaction between the subnetworks of a complex network

Nonlinear fault detection for batch processes via improved chordal kernel tensor locality preserving projections

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