Prediction Intervals for ARIMA Processes: A Sieve Bootstrap Approach

• Activity Number: 406
• Type: Contributed
• Date/Time: Tuesday, July 31, 2012 : 2:00 PM to 3:50 PM
• Sponsor: Business and Economic Statistics Section
• Author(s): Maduka Rupasinghe*+ and V A Samaranayake
• Companies: Ashland University and Missouri University of Science and Technology
• Keywords: Unit root processes ; Forecast intervals ; Integrated process ; Nonstationarity

Abstract

The sieve bootstrap is a model-free re-sampling method that approximates an invertible linear process with a finite autoregressive model whose order increases with sample size. Prediction intervals based on this approach have been successfully implemented for stationary invertible ARMA processes. The coverage probabilities of sieve bootstrap intervals developed for ARMA models, however, are well below the nominal level in the presence of a unit root in the autoregressive polynomial. An approach that overcomes this drawback is proposed and the asymptotic properties of the proposed method are derived. Monte Carlo simulation results indicate that the proposed method provides near nominal coverage at moderate sample sizes.