On the Consequences of Power-Law Behavior in Partial Correlation Network Models

30 Pages Posted: 4 Jan 2017 Last revised: 11 Apr 2017

See all articles by Matteo Barigozzi

Matteo Barigozzi

Université Libre de Bruxelles (ULB) - European Center for Advanced Research in Economics and Statistics (ECARES); London School of Economics and Political Science; University of Bologna

Christian T. Brownlees

Universitat Pompeu Fabra - Faculty of Economic and Business Sciences

Gabor Lugosi

Universitat Pompeu Fabra - Department of Economics and Business (DEB)

Date Written: January 2, 2017

Abstract

We study the cross-sectional dependence properties of a partial correlation network model with sparse power-law structure. We show that when the degree distribution of the network 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 a panel of stock returns of a large set of companies listed in the S&P500 and show that the covariance matrix of returns exhibits empirical features that are consistent with our power-law model.

Keywords: Partial Correlation Networks, Random Graphs, Power-Law

JEL Classification: C39, C50, C55

Suggested Citation

Barigozzi, Matteo and Barigozzi, Matteo and Barigozzi, Matteo and Brownlees, Christian T. and Lugosi, Gabor, On the Consequences of Power-Law Behavior in Partial Correlation Network Models (January 2, 2017). Available at SSRN: https://ssrn.com/abstract=2892530 or http://dx.doi.org/10.2139/ssrn.2892530

Matteo Barigozzi

Université Libre de Bruxelles (ULB) - European Center for Advanced Research in Economics and Statistics (ECARES) ( email )

Ave. Franklin D Roosevelt, 50 - C.P. 114
Brussels, B-1050
Belgium

HOME PAGE: http://www.barigozzi.eu/research.html

London School of Economics and Political Science ( email )

Houghton Street
London, England WC2A 2AE
United Kingdom

University of Bologna ( email )

Piazza Scaravilli 2
Bologna, 40100
Italy

Christian T. Brownlees (Contact Author)

Universitat Pompeu Fabra - Faculty of Economic and Business Sciences ( email )

Ramon Trias Fargas 25-27
Barcelona, 08005
Spain

HOME PAGE: http://econ.upf.edu/~cbrownlees/

Gabor Lugosi

Universitat Pompeu Fabra - Department of Economics and Business (DEB) ( email )

Barcelona, 08005
Spain

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