The Conditional Autoregressive F-Riesz Model for Realized Covariance Matrices

Anne Opschoor, André Lucas and Luca Rossini

Journal of Financial Econometrics, 2025, vol. 23, issue 2, 177-190

Abstract: We introduce a new model for the dynamics of fat-tailed (realized) covariance-matrix-valued time-series using the F-Riesz distribution. The model allows for heterogeneous tail behavior across the coordinates of the covariance matrix via two vector-valued degrees of freedom parameters, thus generalizing the familiar Wishart and matrix-F distributions. We show that the filter implied by the new model is invertible and that a two-step targeted maximum likelihood estimator is consistent. Applying the new F-Riesz model to U.S. stocks, both tail heterogeneity and tail fatness turn out to be empirically relevant: they produce significant in-sample and out-of-sample likelihood increases, ex-post portfolio standard deviations that are in the global minimum variance model confidence set, and economic differences that are either in favor of the new model or competitive with a range of benchmark models.

Keywords: covariance matrix distributions; tail heterogeneity; (Inverse) Riesz distribution; fat-tails; realized covariance matrices (search for similar items in EconPapers)
JEL-codes: C32 C58 G17 (search for similar items in EconPapers)
Date: 2025
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