Prediction intervals in the ARFIMA model using bootstrap G

Glaura C. Franco, Gustavo C. Lana, Valderio A. Reisen

Abstract


This paper presents a bootstrap resampling scheme to build pre-
diction 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 estima-
tion. Bootstrap procedures, as nonparametric methods, can overcome
these diculties. In this paper, we test two bootstrap prediction in-
tervals 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 boot-
strap, (Thombs and Schucany, 1990; Pascual et al., 2004), never used
for ARFIMA models to the knowlegde of the authors. For the second
approach, 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, through
a Monte Carlo experiment, to the asymptotic interval, under Gaus-
sian 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 ap-
plication to real data of temperature in New York city is also presented
to illustrate the procedures.


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DOI: http://dx.doi.org/10.24294/fsj.v1i3.687

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