Cholesky GAS models for large time-varying covariance matrices

This paper develops a new class of multivariate models for large-dimensional time-varying covariance matrices, called Cholesky generalized autoregressive score (GAS) models, which are based on the Cholesky decomposition of the covariance matrix and assume that the parameters are score-driven. Specifically, two types of score-driven updates are considered: one is closer to the GARCH family, and the other is inspired by the stochastic volatility model. We demonstrate that the models can be estimated equation-wise and are computationally feasible for high-dimensional cases. Moreover, we design an equation-wise dynamic model averaging or selection algorithm which simultaneously extracts model and parameter uncertainties, equipped with dynamically estimated model parameters. The simulation results illustrate the superiority of the proposed models. Finally, using a sizeable daily return dataset that includes 124 sectors in the Chinese stock market, two empirical studies with a small sample and a full sample are conducted to verify the advantages of our models. The full sample analysis by a dynamic correlation network documents significant structural changes in the Chinese stock market before and after COVID-19.