Improved Prediction Limits For AR(p) and ARCH(p) Processes

A new simulation-based prediction limit that improves on any given estimative d-step-ahead prediction limit for a Markov process is described. This improved prediction limit can be found with almost no algebraic manipulations. Nonetheless, it has the same asymptotic coverage properties as the Barndorff-Nielsen and Cox [Inference and Asymptotics (1994) Chapman and Hall, London] and Vidoni [Journal of Time Series Analysis Vol. 25, pp. 137-154.] (2004) improved prediction limits. The new simulation-based prediction limit is ideally suited to those Markov process models for which the algebraic manipulations required for the latter improved prediction limits are very complicated. We illustrate the new method by applying it in the context of one-step-ahead prediction for a zero-mean Gaussian AR(2) process and an ARCH(2) process. Copyright 2007 The Authors