Expansions for Approximate Maximum Likelihood Estimators of the Fractional Difference Parameter

Offer Lieberman and Peter Phillips
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Offer Lieberman: Technion-Israel Institute of Technology

No 1474, Cowles Foundation Discussion Papers from Cowles Foundation for Research in Economics, Yale University

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).

Keywords: Bootstrap; Edgeworth expansion; Fractional differencing; Pivotal statistic (search for similar items in EconPapers)
JEL-codes: C13 C22 (search for similar items in EconPapers)
Pages: 19 pages
Date: 2004-07
New Economics Papers: this item is included in nep-ecm and nep-ets
Note: CFP 1157.
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Citations: View citations in EconPapers (4)

Published in Econometrics Journal (2005), 8: 367-379

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