Bayesian Tail Risk Forecasting using Realised Volatility DCC-Copula-GARCH Models

A Skewed Student-t Realised DCC copula model using Realised Volatility GARCH marginal functions is developed within a Bayesian framework for the purpose of forecasting portfolio Value at Risk and Conditional Value at Risk. The use of copulas is implemented so that the marginal distributions can be separated from the dependence structure to produce tail forecasts. This is compared to using traditional GARCH-copula models, and GARCH on an aggregated portfolio, with weekly returns of five financial assets spanning from March 1971 to May 2014. An initial sample of 773 weeks is used to estimate the models, while 1000 one-week ahead forecasts are produced to compare out-of-sample forecast performance. Copula models implementing a Realised Volatility GARCH framework show an improvement over traditional GARCH models over a variety of formal and informal tests.