Summary
This paper considers different bootstrap procedures for investigating the estimation of the fractional parameter d in a particular case of long memory processes, i.e. for ARFIMA models withd in (0.0, 0.5). We propose two bootstrap techniques to deal with semiparametric estimation methods of d. One approach consists of the local bootstrap method for time frequency initially suggested for the ARMA case by Paparoditis and Politis (1999), and the other consists of the bootstrapping in the residuals of the frequency-domain regression equation. Through Monte Carlo simulation, these alternative bootstrap methods are compared, based on the mean and the mean square error of the estimators, with the well-known parametric and nonparametric bootstrap techniques for time series models.
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Acknowledgments
V.A. Reisen gratefully acknowledges CNPq/Brazil and G.C. Franco acknowledges CNPq/Brazil and FAPEMIG (CEX-855/98) for the partial financial support. The authors thank the editor (W. Hardle) and the anonymous referees for their valuable contributions.
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Franco, G.C., Reisen, V.A. Bootstrap techniques in semiparametric estimation methods for ARFIMA models: A comparison study. Computational Statistics 19, 243–259 (2004). https://doi.org/10.1007/BF02892059
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DOI: https://doi.org/10.1007/BF02892059