### Abstract:

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.

Speaker

Associate Professor Paul Kabaila

Research Area

Statistics Seminar

Affiliation

La Trobe University

Date

Fri, 20/02/2009 - 4:00pm

Venue

RC-4082