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Expansions for Approximate Maximum Likelihood Estimators of the Fractional Difference Parameter

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Abstract

This paper derives second-order expansions for the distributions of the Whittle and profile plug-in maximum likelihood estimators of the fractional difference parameter in the ARFIMA(0,d,0) with unknown mean and variance. Both estimators are shown to be second-order pivotal. This extends earlier findings of Lieberman and Phillips (2001), who derived expansions for the Gaussian maximum likelihood estimator under the assumption that the mean and variance are known. One implication of the results is that the parametric bootstrap upper one-sided confidence interval provides an o(n^{-1}ln n) improvement over the delta method. For statistics that are not second-order pivotal, the improvement is generally only of the order o(n^{-1/2}ln n).

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Bibliographic Info

Paper provided by Cowles Foundation for Research in Economics, Yale University in its series Cowles Foundation Discussion Papers with number 1474.

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Length: 19 pages
Date of creation: Jul 2004
Date of revision:
Publication status: Published in Econometrics Journal (2005), 8: 367-379
Handle: RePEc:cwl:cwldpp:1474

Note: CFP 1157.
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Keywords: Bootstrap; Edgeworth expansion; Fractional differencing; Pivotal statistic;

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Cited by:
  1. Offer Lieberman & Peter C.B. Phillips, 2006. "A Complete Asymptotic Series for the Autocovariance Function of a Long Memory Process," Cowles Foundation Discussion Papers 1586, Cowles Foundation for Research in Economics, Yale University.
  2. Offer Lieberman & Peter Phillips, 2008. "Refined Inference on Long Memory in Realized Volatility," Econometric Reviews, Taylor & Francis Journals, vol. 27(1-3), pages 254-267.
  3. Gao, Jiti, 2007. "Nonlinear time series: semiparametric and nonparametric methods," MPRA Paper 39563, University Library of Munich, Germany, revised 01 Sep 2007.

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