Open Access
Translator Disclaimer
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


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.


Download Citation

L. Giraitis. P.M. Robinson. "Edgeworth expansions for semiparametric Whittle estimation of long memory." Ann. Statist. 31 (4) 1325 - 1375, August 2003.


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

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

Primary: 62G20
Secondary: 62M10

Keywords: Edgeworth expansion , long memory , semiparametric approximation

Rights: Copyright © 2003 Institute of Mathematical Statistics


Vol.31 • No. 4 • August 2003
Back to Top