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August 2003 Edgeworth expansions for semiparametric Whittle estimation of long memory
L. Giraitis, P.M. Robinson
Ann. Statist. 31(4): 1325-1375 (August 2003). DOI: 10.1214/aos/1059655915

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.

Citation

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L. Giraitis. P.M. Robinson. "Edgeworth expansions for semiparametric Whittle estimation of long memory." Ann. Statist. 31 (4) 1325 - 1375, August 2003. https://doi.org/10.1214/aos/1059655915

Information

Published: August 2003
First available in Project Euclid: 31 July 2003

zbMATH: 1041.62012
MathSciNet: MR2001652
Digital Object Identifier: 10.1214/aos/1059655915

Subjects:
Primary: 62G20
Secondary: 62M10

Rights: Copyright © 2003 Institute of Mathematical Statistics

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Vol.31 • No. 4 • August 2003
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