Title: Improved bootstrap simultaneous prediction intervals for autoregressive models
Abstract: The specification of well-calibrated multivariate prediction regions may be useful in time series applications, whenever the aim is to consider not just one single forecast but a group of consecutive forecasts. However, the definition of multivariate prediction regions, having coverage probability closed to the target nominal value, is still a challenging problem both from the theoretical and the practical point of view. An important result on improved multivariate prediction, based on higher-order asymptotic calculations, is reviewed. Although this solution is asymptotically superior to the estimative one, which is simpler but it may lead to unreliable predictive conclusions, it is usually hard to apply, since it requires complicated asymptotic expansions. A new asymptotically equivalent solution, giving improved simultaneous prediction intervals, is presented. It has a simple and intuitive form and, when computations are hard to perform, it is readily available an approximation based on bootstrap simulation methods. An application of this simple bootstrap-based procedure to autoregressive time series models is presented.
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