Tail Heterogeneity for Dynamic Covariance Matrices: the F-Riesz Distribution

We introduce a novel model for the dynamics of fat-tailed (realized) covariance-matrix-valued time series using the new F-Riesz distribution. The model allows for different 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 by introducing heterogeneous tail behavior. 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 are empirically relevant and produce large in-sample and out-of-sample likelihood increases and lower ex-post portfolio standard deviations compared to static models or models with homogeneous tail behavior