406 – Seasonal Time Series, Goodness-of-Fit, and Unit Root
Prediction Intervals for ARIMA Processes: Sieve Bootstrap Approach
Maduka Rupasinghe
Ashland University
V. A. Samaranayake
Missouri University of Science and Technology
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.
