We study the effect of parameter and model uncertainty on the left‐tail of predictive densities and in particular on VaR forecasts. To this end, we evaluate the predictive performance of several GARCH‐type models estimated via Bayesian and maximum likelihood techniques. In addition to individual models, several combination methods are considered, such as Bayesian model averaging and (censored) optimal pooling for linear, log or beta linear pools. Daily returns for a set of stock market indexes are predicted over about 13 years from the early 2000s. We find that Bayesian predictive densities improve the VaR backtest at the 1% risk level for single models and for linear and log pools. We also find that the robust VaR backtest exhibited by linear and log pools is better than the backtest of single models at the 5% risk level. Finally, the equally weighted linear pool of Bayesian predictives tends to be the best VaR forecaster in a set of 42 forecasting techniques.
Density forecast combination is a useful tool for risk managers to reduce model risk. We present up‐to‐date methodologies in the field, discuss key issues, and provide some illustrations.
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