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Invariance of the first difference in ARFIMA models

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Abstract

A desirable property for an estimator of the fractional ARFIMA parameter is to be first difference invariant. This paper investigates the effects on the fractional parameter estimator in nonstationary ARFIMA(p,d,q) processes before and after applying a first difference. We consider semiparametric and parametric approaches for estimating d. The study is based on a Monte Carlo simulation for different sample sizes. The Brazilian exchange rate series is given as an application of the methodology.

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Acknowledgments

V.A. Reisen was partially supported by CNPq-Brazil. S.R.C. Lopes was partially supported by CNPq-Brazil and by Pronex Probabilidade e Processos Estocásticos (Convênio MCT/CNPq/FAPERJ — Edital 2003). S.R.C. Lopes and B.P. Olbermann were partially supported by Fundação de Amparo à Pesquisa no Estado do Rio Grande do Sul (FAPERGS Foundation). The authors would like to thank the editor and the anonymous referee for their valuable comments and suggestions that improved this version of the manuscript.

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Authors and Affiliations

  1. Faculdade de Matemática, PUCRS, Av. Ipiranga, 6681, 90619-900, Porto Alegre, RS, Brazil

    Barbara P. Olbermann

  2. Instituto de Matemática, UFRGS, Av. Bento Gonçalves, 9500, 91509-900, Porto Alegre, RS, Brazil

    Sílvia R. C. Lopes

  3. Departamento de Estatística, UFES, Av. Fernando Ferrari, s/n, 29060-900, Vitória, ES, Brazil

    Valdério A. Reisen

Authors
  1. Barbara P. Olbermann
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  2. Sílvia R. C. Lopes
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  3. Valdério A. Reisen
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Correspondence to Sílvia R. C. Lopes.

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Olbermann, B.P., Lopes, S.R.C. & Reisen, V.A. Invariance of the first difference in ARFIMA models. Computational Statistics 21, 445–461 (2006). https://doi.org/10.1007/s00180-006-0005-0

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  • DOI: https://doi.org/10.1007/s00180-006-0005-0

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