Prediction intervals in the ARFIMA model using bootstrap G

Abstract

This paper presents a bootstrap resampling scheme to build pre-diction intervals for future values in fractionally autoregressive movingaverage (ARFIMA) models. Standard techniques to calculate forecastintervals rely on the assumption of normality of the data and do nottake into account the uncertainty associated with parameter estima-tion. Bootstrap procedures, as nonparametric methods, can overcomethese diculties. In this paper, we test two bootstrap prediction in-tervals based on the nonparametric bootstrap in the residuals of theARFIMA model. In this paper, two bootstrap prediction intervals areproposed based on the nonparametric bootstrap in the residuals ofthe ARFIMA model. The rst one is the well known percentile boot-strap, (Thombs and Schucany, 1990; Pascual et al., 2004), never usedfor ARFIMA models to the knowlegde of the authors. For the secondapproach, the intervals are calculated using the quantiles of the empir-ical distribution of the bootstrap prediction errors (Masarotto, 1990;Bisaglia e Grigoletto, 2001). The intervals are compared, througha Monte Carlo experiment, to the asymptotic interval, under Gaus-sian and non-Gaussian error distributions. The results show that thebootstrap intervals present coverage rates closer to the nominal levelassumed, when compared to the asymptotic standard method. An ap-plication to real data of temperature in New York city is also presentedto illustrate the procedures.