Summary This paper demonstrates the cases where bootstrap does not work for heteroscedastic time series models. We construct prediction intervals for the ARMA-GARCH models using bootstrap and see how a wrong application of bootstrap could lead to a false conclusion

In this paper we introduce the nonparametric AR(1)–ARCH(1) model and show weak consistency of the Nadaraya–Watson estimators for the model. We propose a residual and a wild bootstrap method and prove weak consistency of the bootstrap estimators.