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
Date Written: January 22, 2021
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: Suggested Citation