Forecasting nonlinear time series with neural network sieve bootstrap

A new method to construct nonparametric prediction intervals for nonlinear time series data is proposed. Within the frameworkof the recently developed sieve bootstrap, the new approach employs neural network models to approximate the original nonlinearprocess. The method is flexible and easy to implement as a standard residual bootstrap scheme while retaining the advantage ofbeing a nonparametric technique. It is model-free within a general class of nonlinear processes and avoids the specification of afinite dimensional model for the data generating process. The results of a Monte Carlo study are reported in order to investigate thefinite sample performances of the proposed procedure.