Bootstrap Prediction Interval for ARMA Models with Unknown Orders

Abstract

This paper aims to investigate the construction of the prediction intervals for ARMA (p, q) models with unknown orders. We present the bootstrap algorithms for the prediction intervals based on the bootstrap distribution of orders (p, q). The asymptotic properties of the intervals are also discussed. The Monte Carlo simulation studies show that the proposed algorithm significantly improves the coverage accuracy of the prediction interval compared to the methods using pre-estimated values of orders, especially when the sample size is small and the true model order is low.