Predicting Using Box-Jenkins, Nonparametric, and Bootstrap Techniques

Abstract

In this article, a new semiparametric prediction system is presented for time series. The prediction method incorporated to the system consists of a nonparametric part that estimates the trend, a Box–Jenkins prediction of the residual series, and some bootstrap methodology to construct prediction intervals. Consistency of the estimators proposed for the autoregression function and the parameters in the Box–Jenkins model and the validity of a new bootstrap resampling plan adapted to autoregressive integrated models are proved. The Monte Carlo simulation study, as well as the applications to real data (carried out with the automated system, incorporating the method, developed for predicting concentration levels in the surroundings of a Spanish power station), show that this method outperforms other standard competitors.