Bootstrap Predictive Inference for Arima Processes

Abstract

We introduce a new bootstrap strategy to obtain prediction intervals inARIMA (P,d,l) processes. Its main advantages over previous resampling proposals for ARI (P,d) models are that it incorporates variability due to parameter estimation and it makes unnecessary the process backward representation to resample the series. Consequently, the method is very flexible and can be extended to general models not having a backward representation. Moreover, our bootstrap technique allows to obtain the prediction density of processes with moving average components. Its implementation is computationally very simple. The asymptotic properties of the bootstrap prediction distributions are proved. Extensive finite sample Monte Carlo experiments are carried out to compare the performance of this method versus alternative techniques for ARI (P,d) processes. Our method either behaves similarly or outperforms in most cases previous proposals.