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Giraitis, L.; Robinson, P. M.

Edgeworth expansions for semiparametric Whittle estimation of long memory. (English) Zbl 1041.62012

Ann. Stat. 31, No. 4, 1325-1375 (2003).
Summary: 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.

Cited in 18 Documents

MSC:

62E20 Asymptotic distribution theory in statistics
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62G20 Asymptotic properties of nonparametric inference

Keywords:

empirical expansions; bias correction
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Full Text: DOI Euclid

References:

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