Bootstrap Prediction in Univariate Volatility Models with Leverage Effect

The EGARCH and GJR-GARCH models are widely used in modeling volatility when a leverage effect is present in the data. Traditional methods of constructing prediction intervals for time series normally assume that the model parameters are known, and the innovations are normally distributed. When these assumptions are not true, the prediction interval obtained usually has the wrong coverage. In this article, the Pascual, Romo and Ruiz (PPR) algorithm, developed to obtain prediction intervals for GARCH models, is adapted to obtain prediction intervals of returns and volatility in EGARCH and GJR-GARCH models. These adjustments have the same advantage of the original PRR algorithm, which incorporates a component of uncertainty due to parameter estimation and does not require assumptions about the distribution of the innovations. The adaptations showed good performance in Monte Carlo experiments. However, the performance, especially in volatility prediction, can be very poor in the presence an additive outlier near the forecasting origin. The algorithms are applied to the daily return's series of the São Paulo Stock Market Index