Robust sieve bootstrap prediction intervals for contaminated time series

Time series prediction is of primary importance in a variety of applications from several science fields, like engineering, finance, earth sciences, etc. Time series prediction can be divided in to two main tasks, point and interval estimation. Estimating prediction intervals, is in some cases more important than point estimation mainly because it indicates the likely uncertainty in the prediction process. 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 different types of outliers is not robust from a distributional point of view, leading to an undesirable increase in the length of the prediction intervals. In the analysis of time series, it is common to have irregular observations that have different types of outliers. For this reason, we propose the construction of prediction intervals for returns based on the winsorized residual and bootstrap techniques for time series prediction. We propose a novel, simple and distribution free resampling technique for developing robust prediction intervals for returns and volatilities for GARCH models. The proposed procedure is illustrated by an application to known synthetic and real-time series.