Sieve bootstrap prediction intervals for contaminated non-linear processes

Recently, the sieve bootstrap method has been successfully used in prediction of nonlinear time series. In this work we study the performance of the prediction intervals based on the sieve bootstrap technique, which does not require the distributional assumption of normality as most techniques that are found in the literature. The construction of prediction intervals in the presence of patchy outliers are not robust from a distributional point of view, leading to an undesirable increase in the length of the prediction intervals. In the analysis of financial time series it is common to have irregular observations that have different types of outliers, isolated and in groups. For this reason we propose the construction of prediction intervals for returns based in the winsorized residual and bootstrap techniques for financial time series. We propose a novel, simple, efficient and distribution free resampling technique for developing robust prediction intervals for returns and volatilities for TGARCH models. The proposed procedure is illustrated by an application to known synthetic time series.