Prediction Intervals in ARCH Models Using Sieve Bootstrap Robust Against Outliers

One of the primary goals of time series (TS) modeling is to forecast future observations. Although point forecasts are the most common type of prediction, interval forecasts are more informative and are typically obtained as prediction intervals (PIs). For non-linear TS data, the ARCH model is one of the widely used models. The Sieve Bootstrap method is a popular method for constructing PIs in TS models. The TS data are not always free from outliers, whose presence may result in an increase in the length of PIs obtained also with poor coverage. In this study, two new robust Sieve Bootstrap approaches based on weighted least squares estimation have been proposed to deal with the presence of outliers for developing PIs for both returns and volatilities in the ARCH model setup. The performances of the proposed methods viz., Robust Unconditional Sieve Bootstrap (RUSB) and Robust Sieve Bootstrap (RSB) for constructing PIs using both simulated as well as real data sets have been found to be better when compared with their existing counterparts.