Prediction intervals in the ARFIMA model using bootstrap G

Abstract

This paper presents a bootstrap resampling scheme to build prediction intervals for future values in fractionally autoregressive moving average (ARFIMA) models. Standard techniques to calculate forecast intervals rely on the assumption of normality of the data and do not take into account the uncertainty associated with parameter estimation. Bootstrap procedures, as nonparametric methods, can overcome these diculties. In this paper, we test two bootstrap prediction intervals based on the nonparametric bootstrap in the residuals of the ARFIMA model. In this paper, two bootstrap prediction intervals are proposed based on the nonparametric bootstrap in the residuals of the ARFIMA model. The rst one is the well known percentile bootstrap, (Thombs and Schucany, 1990; Pascual et al., 2004), never used for ARFIMA models to the knowledge of the authors. For the second approach, the intervals are calculated using the quantiles of the empirical distribution of the bootstrap prediction errors (Masarotto, 1990; Bisaglia e Grigoletto, 2001). The intervals are compared, through a Monte Carlo experiment, to the asymptotic interval, under Gaussian and non-Gaussian error distributions. The results show that the bootstrap intervals present coverage rates closer to the nominal level assumed, when compared to the asymptotic standard method. An application to real data of temperature in New York city is also presented to illustrate the procedures.