Bootstrap approaches and confidence intervals for stationary and non-stationary long-range dependence processes

Glaura C. Franco and Valderio A. Reisen

Physica A: Statistical Mechanics and its Applications, 2007, vol. 375, issue 2, 546-562

Abstract: This paper deals with different bootstrap approaches and bootstrap confidence intervals in the fractionally autoregressive moving average (ARFIMA(p,d,q)) process [J. Hosking, Fractional differencing, Biometrika 68(1) (1981) 165–175] using parametric and semi-parametric estimation techniques for the memory parameter d. The bootstrap procedures considered are: the classical bootstrap in the residuals of the fitted model [B. Efron, R. Tibshirani, An Introduction to the Bootstrap, Chapman and Hall, New York, 1993], the bootstrap in the spectral density function [E. Paparoditis, D.N Politis, The local bootstrap for periodogram statistics. J. Time Ser. Anal. 20(2) (1999) 193–222], the bootstrap in the residuals resulting from the regression equation of the semi-parametric estimators [G.C Franco, V.A Reisen, Bootstrap techniques in semiparametric estimation methods for ARFIMA models: a comparison study, Comput. Statist. 19 (2004) 243–259] and the Sieve bootstrap [P. Bühlmann, Sieve bootstrap for time series, Bernoulli 3 (1997) 123–148]. The performance of these procedures and confidence intervals for d in the stationary and non-stationary ranges are empirically obtained through Monte Carlo experiments. The bootstrap confidence intervals here proposed are alternative procedures with some accuracy to obtain confidence intervals for d.

Keywords: Semi-parametric and parametric procedures; Fractionally integrated ARMA process; Bootstrap (search for similar items in EconPapers)
Date: 2007
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Citations: View citations in EconPapers (5)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:375:y:2007:i:2:p:546-562

DOI: 10.1016/j.physa.2006.08.027

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