Multivariate Semi-nonparametric Distributions with Dynamic Conditional Correlations

This paper generalizes the Dynamic Conditional Correlation (DCC) model of Engle (2002) incorporating a flexible non-Gaussian distribution based on Gram-Charlier expansions. The resulting semi-nonparametric (SNP)-DCC model admits estimation in two stages and deals with the negativity problem inherent to truncated SNP densities. We test the performance of a SNP-DCC model with respect to the (Gaussian)-DCC through an empirical application of density forecasting for portfolio returns. Our results show that the proposed multivariate model provides a better in-sample fit and forecast of the portfolio returns distribution, being thus useful for financial risk forecasting and evaluation