Power-law partial correlation network models

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• dc.contributor.author Barigozzi, Matteo
• dc.contributor.author Brownlees, Christian, 1979-
• dc.contributor.author Lugosi, Gábor
• dc.date.accessioned 2020-06-02T08:59:30Z
• dc.date.available 2020-06-02T08:59:30Z
• dc.date.issued 2018
• dc.description.abstract We introduce a class of partial correlation network models whose network structure is determined by a random graph. In particular in this work we focus on a version of the model in which the random graph has a power-law degree distribution. A number of cross-sectional dependence properties of this class of models are derived. The main result we establish is that when the random graph is power-law, the system exhibits a high degree of collinearity. More precisely, the largest eigenvalues of the inverse covariance matrix converge to an affine function of the degrees of the most interconnected vertices in the network. The result implies that the largest eigenvalues of the inverse covariance matrix are approximately power-law distributed, and that, as the system dimension increases, the eigenvalues diverge. As an empirical illustration we analyse two panels of stock returns of companies listed in the S&P 500 and S&P 1500 and show that the covariance matrices of returns exhibits empirical features that are consistent with our power-law model.en
• dc.description.sponsorship C. Brownlees and G. Lugosi acknowledge financial support from Spanish Ministry of Science and Technology (Grant MTM2015-67304-P) and from Spanish Ministry of Economy and Competitiveness, through the Severo Ochoa Programme for Centres of Excellence in R&D (SEV-2011-0075). G. Lugosi was supported by “High-dimensional problems in structured probabilistic models - Ayudas Fundación BBVA a Equipos de Investigación Cientifica 2017” and by “Google Focused Award Algorithms and Learning for AI”.
• dc.format.mimetype application/pdf
• dc.identifier.citation Barigozzi M, Brownless C, Lugosi G. Power-law partial correlation network models. Electron J Statist. 2018 Sep 18;12(2):2905-29. DOI: 10.1214/18-EJS1478
• dc.identifier.doi http://dx.doi.org/10.1214/18-EJS1478
• dc.identifier.issn 1935-7524
• dc.identifier.uri http://hdl.handle.net/10230/44869
• dc.language.iso eng
• dc.publisher The Institute of Mathematical Statistics and the Bernoulli Society
• dc.relation.ispartof Electronic Journal of Statistics. 2018 Sep 18;12(2):2905-29
• dc.relation.projectID info:eu-repo/grantAgreement/ES/1PE/MTM2015-67304-P
• dc.rights Copyright for all articles in EJP is CC BY 4.0.
• dc.rights.accessRights info:eu-repo/semantics/openAccess
• dc.rights.uri https://creativecommons.org/licenses/by/4.0/
• dc.subject.keyword Partial correlationen
• dc.subject.keyword Networks random graphsen
• dc.subject.keyword Power-lawen
• dc.title Power-law partial correlation network modelsen
• dc.type info:eu-repo/semantics/article
• dc.type.version info:eu-repo/semantics/publishedVersion