Bootstrap Prediction Interval For ARMA Models With Unknown Orders

When modeling and forecasting problems,many details of the model will be un-known.This thesis aims to discuss the construction algorithm for prediction intervals when model orders are unknown under the ARMA model setting.Previous work on the order selection of ARMA models is very mature,and effective Bootstrap algorithms ex-ist for the prediction intervals under regression models and AR(p)models.This thesis first introduces the most commonly used AIC criterion for order selection and the cor-responding Bootstrap algorithm.Then,under the ARMA model,this thesis presents a coherent prediction interval Bootstrap algorithm,and proves that this algorithm can simultaneously capture model estimation errors and random errors.For an ARMA model with unknown orders,this thesis proposes a prediction interval Bootstrap algo-rithm based on the conditional distribution of orders(p,q)instead of pre-estimated values of p and q.Compared with previous work,this proposed algorithm has better coverage and robustness.Its asymptotic properties are also proved.In the simulations,using four datasets of randomly generated ARMA models,this thesis compares the proposed Bootstrap algorithm based on predictive roots with three other methods-the Bootstrap algorithm based on percentile method,the Bootstrap algorithm based on conditional distribution,and the Bootstrap algorithm based on predefined p and q.The simulation results show that,compared with other algorithm,the proposed Bootstrap algorithm has significantly improved the coverage accuracy of the prediction interval,and has better robustness especially when the orders p and q cannot be accurately estimated or the data size is very small.