Tail Heterogeneity for Dynamic Covariance-Matrix-Valued Random Variables: the F-Riesz Distribution

Tinbergen Institute Discussion Paper 2021-010/III

38 Pages Posted: 13 Mar 2021

See all articles by Francisco Blasques

Francisco Blasques

VU University Amsterdam; Tinbergen Institute

Andre Lucas

Vrije Universiteit Amsterdam - School of Business and Economics; Tinbergen Institute

Anne Opschoor

Vrije Universiteit Amsterdam

Luca Rossini

University of Milan; Ca Foscari University of Venice - Dipartimento di Economia

Date Written: January 22, 2021

Abstract

We introduce the new F-Riesz distribution to model tail-heterogeneity in fat-tailed covariance matrix observations. In contrast to the typical matrix-valued distributions from the econometric literature, the F-Riesz distribution allows for different tail behavior across all variables in the system. We study the consistency properties of the maximum likelihood estimator in both static and dynamic models with F- Riesz innovations using both one-step and two-step (targeting) estimation techniques. Allowing for tail-heterogeneity when modeling covariance matrices appears empirically highly relevant. When applying the new distribution to realized covariance matrices of 30 U.S. stocks over a 14 year period, we find huge likelihood increases both in-sample and out-of-sample compared to all competing distributions, including the Wishart, inverse Wishart, Riesz, inverse Riesz, and matrix-F distribution.

Keywords: Matrix Distributions, Tail Heterogeneity, (inverse) Riesz Distribution, Fat-Tails, Realized Covariance Matrices

JEL Classification: C58, C32, C46

Suggested Citation

Blasques, Francisco and Lucas, Andre and Opschoor, Anne and Rossini, Luca, Tail Heterogeneity for Dynamic Covariance-Matrix-Valued Random Variables: the F-Riesz Distribution (January 22, 2021). Tinbergen Institute Discussion Paper 2021-010/III, Available at SSRN: https://ssrn.com/abstract=3772162 or http://dx.doi.org/10.2139/ssrn.3772162

Francisco Blasques (Contact Author)

VU University Amsterdam ( email )

De Boelelaan 1105
Amsterdam, ND North Holland 1081 HV
Netherlands

Tinbergen Institute ( email )

Gustav Mahlerplein 117
Amsterdam, 1082 MS
Netherlands

Andre Lucas

Vrije Universiteit Amsterdam - School of Business and Economics ( email )

De Boelelaan 1105
Amsterdam, 1081 HV
Netherlands
+31 20 598 6039 (Phone)
+31 20 598 6020 (Fax)

HOME PAGE: http://personal.vu.nl/a.lucas

Tinbergen Institute

Roetersstraat 31
Amsterdam, 1018 WB
Netherlands

HOME PAGE: http://www.tinbergen.nl

Anne Opschoor

Vrije Universiteit Amsterdam ( email )

De Boelelaan 1105
Amsterdam, NL 1081 HV
Netherlands

Luca Rossini

University of Milan ( email )

Via Festa del Perdono, 7
Milan, 20122
Italy

Ca Foscari University of Venice - Dipartimento di Economia ( email )

Cannaregio 873
Venice, 30121
Italy

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