## The Annals of Statistics

### Edgeworth expansions for semiparametric Whittle estimation of long memory

#### 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.

#### Article information

Source
Ann. Statist., Volume 31, Number 4 (2003), 1325-1375.

Dates
First available in Project Euclid: 31 July 2003

https://projecteuclid.org/euclid.aos/1059655915

Digital Object Identifier
doi:10.1214/aos/1059655915

Mathematical Reviews number (MathSciNet)
MR2001652

Zentralblatt MATH identifier
1041.62012

Subjects
Primary: 62G20: Asymptotic properties

#### Citation

Giraitis, L.; Robinson, P.M. Edgeworth expansions for semiparametric Whittle estimation of long memory. Ann. Statist. 31 (2003), no. 4, 1325--1375. doi:10.1214/aos/1059655915. https://projecteuclid.org/euclid.aos/1059655915

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