Partial Directed Coherence and the Vector Autoregressive Modelling Myth and a Caveat

Luiz A Baccalá; Koichi Sameshima

doi:10.3389/fnetp.2022.845327

Partial Directed Coherence and the Vector Autoregressive Modelling Myth and a Caveat

Front Netw Physiol. 2022 Apr 28:2:845327. doi: 10.3389/fnetp.2022.845327. eCollection 2022.

Authors

Luiz A Baccalá¹, Koichi Sameshima²

Affiliations

¹ Laboratório de Comunicações e Sinais, Departamento de Telecomunicações e Controle, Escola Politécnica, Universidade de São Paulo, São Paulo, Brazil.
² Departamento de Radiologia e Oncologia, Faculdade de Medicina, Universidade de São Paulo, São Paulo, Brazil.

Abstract

Here we dispel the lingering myth that Partial Directed Coherence is a Vector Autoregressive (VAR) Modelling dependent concept. In fact, our examples show that it is spectral factorization that lies at its heart, for which VAR modelling is a mere, albeit very efficient and convenient, device. This applies to Granger Causality estimation procedures in general and also includes instantaneous Granger effects. Care, however, must be exercised for connectivity between multivariate data generated through nonminimum phase mechanisms as it may possibly be incorrectly captured.

Keywords: Granger causality; nonminimum phase systems; partial directed coherence; spectral factorization; time series connectivity modelling; total partial directed coherence.

Grants and funding

LB was funded by CNPq, Grant number 308073/2017-7. LB and KS were partially supported by FAPESP Grant 2017/12943-8.