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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 1/√m (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
Institution: The University of York
Academic Units: The University of York > Mathematics (York)
The University of York > Economics and Related Studies (York)
Depositing User: York RAE Import
Date Deposited: 28 Aug 2009 10:43
Last Modified: 28 Aug 2009 10:43
Published Version: http://dx.doi.org/10.1214/aos/1059655915
Status: Published
Publisher: Institute of Mathematical Statistics
Identification Number: 10.1214/aos/1059655915
URI: http://eprints.whiterose.ac.uk/id/eprint/5614

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