Robust bootstrap forecast densities for GARCH models: returns, volatilities and value-at-risk

Abstract

Bootstrap procedures are useful in GARCH models to obtain forecast densities for returns and volatilities.In this paper, we analyze the effect of outliers on the finite sample properties of these densities when they are based on standard maximum likelihood and robust procedures. We show that when the former procedure is implemented, the bootstrap densities are badly affected by the presence of outliers. However,the robust estimator based on variance targeting with an adequate modification of the volatility filter has the best performance when compared with alternative robust procedures. The results are illustrated withboth simulated and real data