Computationally Efficient Bootstrap Prediction Intervals for Returns and Volatilities in ARCH and GARCH Processes

Wepropose a novel, simple, efficient and distribution-free re-sampling technique for developing prediction intervals for returns and volatilities following ARCH/GARCH models. In particular, our key idea is to employ a Box-Jenkins linear representation of an ARCH/GARCH equation and then to adapt a sieve bootstrap procedure to the non-linear GARCH framework. Our simulation studies indicate that the new re-sampling method provide sharp and well calibrated prediction intervals for both returns and volatilities while reducing computational costs up to 100 times, compared to other available re-sampling techniques for ARCH/GARCH models. The proposed procedure is illustrated by application to Yen/U.S dollar daily exchange rate data.