# 13-060/III (2013-04-15; 2014-03-06)

Lukasz Gatarek, Econometric Institute, Erasmus School of Economics, Erasmus University Rotterdam; Lennart Hoogerheide, VU University Amsterdam; Koen Hooning, Delft University of Technology; Herman K. van Dijk, Econometric Institute, Erasmus University Rotterdam, and VU University Amsterdam
censored likelihood, censored posterior, censored predictive likelihood, Bayesian Model Averaging, Value at Risk, Metropolis-Hastings algorithm.
JEL codes:
C11, C15, C22, C51, C53, C58, G17

Accurate prediction of risk measures such as Value at Risk (VaR) and Expected Shortfall (ES) requires precise estimation of the tail of the predictive distribution. Two novel concepts are introduced that offer a specific focus on this part of the predictive density: the censored posterior, a posterior in which the likelihood is replaced by the censored likelihood; and the censored predictive likelihood, which is used for Bayesian Model Averaging. We perform extensive experiments involving simulated and empirical data. Our results show the ability of these new approaches to outperform the standard posterior and traditional Bayesian Model Averaging techniques in applications of Value-at-Risk prediction in GARCH models.