Edgeworth expansions for semiparametric Whittle estimation of long memory

Giraitis, L. and Robinson, P.M. (2003) Edgeworth expansions for semiparametric Whittle estimation of long memory. Annals of Statistics, 31 (4). pp. 1325-1375. ISSN 0090-5364

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Abstract

The semiparametric local Whittle or Gaussian estimate of the long memory parameter is known to have especially nice limiting distributional properties, being asymptotically normal with a limiting variance that is completely known. However in moderate samples the normal approximation may not be very good, so we consider a refined, Edgeworth, approximation, for both a tapered estimate, and the original untapered one. For the tapered estimate, our higher-order correction involves two terms, one of order m-1/2 (where m is the bandwidth number in the estimation), the other a bias term, which increases in m; depending on the relative magnitude of the terms, one or the other may dominate, or they may balance. For the untapered estimate we obtain an expansion in which, for m increasing fast enough, the correction consists only of a bias term. We discuss applications of our expansions to improved statistical inference and bandwidth choice. We assume Gaussianity, but in other respects our assumptions seem mild.

Item Type:	Article
Official URL:	http://www.imstat.org/aos/
Additional Information:	Published 2003 © Institute of Mathematical Statistics. LSE has developed LSE Research Online so that users may access research output of the School. Copyright © and Moral Rights for the papers on this site are retained by the individual authors and/or other copyright owners. Users may download and/or print one copy of any article(s) in LSE Research Online to facilitate their private study or for non-commercial research. You may not engage in further distribution of the material or use it for any profit-making activities or any commercial gain. You may freely distribute the URL (http://eprints.lse.ac.uk) of the LSE Research Online website.
Divisions:	Economics
Subjects:	H Social Sciences > HA Statistics
Date Deposited:	15 Feb 2008
Last Modified:	11 Sep 2025 06:41
URI:	http://eprints.lse.ac.uk/id/eprint/291

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