A HEAVY model for skewed returns and fat-tailed realized covariances with dynamic shape

We propose a newHigh-Frequency-Based Volatility (HEAVY) Generalized Autoregressive Score (GAS) model with Autoregressive Conditional Density (ARCD) estimation for examining the joint dynamics of fat-tailed and skewed daily returns and realized covariance matrix observations. The proposed HEAVY GAS-ARCD models extends the classical (HEAVY) models. The score dynamics for the unobserved true covariance matrix and shape parameters are specified and formulated by assuming a flexible density (Wishart or matrix-F distribution) for the realized covariance measures and a multivariate skewed Student’s t distribution for the daily returns. The class of score models encompasses many realized volatility score models. The proposed models are estimated by using the maximum likelihood estimation (MLE) method. Furthermore, the parameter restrictions for positive definiteness are formulated, conditions of consistency and asymptotic normality are presented, and Monte Carlo simulation experiments are used to study the precision of MLE. In the application, two group data have been used from the portfolio of U.S. financial assets. The performances of the HEAVY GAS-ARCD models are compared with many realized volatility score benchmarks. Both in-sample and out-of-sample forecasting results support the use of the proposed HEAVY GAS-ARCD models.