We consider h-step-ahead prediction for a time series process satisfying a Markov assumption. Our aim is to find an upper 1-a prediction limit that covers the h-step-ahead value of the time series with probability 1-a; conditional on the appropriate statistic. Such prediction limits are very important in finance (Value at Risk) and inventory control. The standard approach is to use an estimative upper 1- a prediction limit. However, this prediction limit has a conditional coverage probability that is only approximately 1 - a: Barndorff-Nielsen and Cox (1994) and Vidoni (2004) show how to improve this prediction limit analytically, so that its conditional coverage probability is closer to 1 - a: For those cases where the algebraic manipulations required for these methods of improvement become very complicated, we propose a new simulation-based improved prediction limit. This prediction limit requires relatively few algebraic manipulations. Nonetheless, it has the same asymptotic conditional coverage properties as the improved prediction limits of Barndorff-Nielsen and Cox (1994) and Vidoni (2004). The new simulation-based improved prediction limit is readily-applicable to AR and ARCH processes.
About the speaker: Dr Paul Kabaila is Reader and Associate Professor at the Department of Mathematics and Statistics, La Trobe University. His research interests are: time series, model selection, bootstrap, confidence limits from discrete data, the foundations of statistical inference and the rigorous analysis of Monte Carlo simulations.