Efficient Bootstrap Forecast Intervals for Return and Volatility Using the Linear Estimator of Arch Models

In this paper, we construct efficient forecast intervals for autoregressive conditional heteroscedastic (ARCH) models using the bootstrap. Forecast intervals for returns and volatility are constructed using the linear estimator (LE) for ARCH model. An advantage of LE over the widely used quasi maximum likelihood estimator (QMLE) is that its computation is very easy and requires less CPU time which enables us to construct these forecast intervals in quick time. Monte Carlo results show that although both estimators provide good mean coverage, the LE can be considered favourable in terms of its mean lengths close to empirical with low standard errors. The bootstrapped prediction intervals for volatilities capture the asymmetry commonly present in real data sets