Forecasting with bootstrap procedures: incorporating the parameter and distribution uncertainties

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Abstract:  When predicting the future evolution of a given variable, there is an increasing interest in obtaining prediction intervals which incorporate the uncertainty associated with the predictions. Due to their flexibility, bootstrap procedures are often implemented with this purpose. First, they do not rely on severe distributional assumptions. Second, they are able to incorporate the parameter uncertainty. Finally, they are attractive from a computational point of view. Many bootstrap methods proposed in the literature rely on the backward representation which limits their application to models with this representation and reduces their advantages given that it complicates computationally the procedures and could limit the asymptotic results to Gaussian errors. However, this representation is not theoretically needed. Therefore, it is possible to simplify the bootstrap procedures implemented in practice without losing their good properties. The bootstrap procedures to construct prediction intervals that do not rely on the backward representation can be implemented in a very wide range of models without this representation. In particular, they can be implemented in univariate ARMA and GARCH models. Also, extensions to unobserved component models and multivariate VARMA models will be considered. Several applications with simulated and real data will be used to illustrate the procedures.