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Expansions for Approximate Maximum Likelihood Estimators of the Fractional Difference Parameter

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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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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
Publication status: Published in Econometrics Journal (2005), 8: 367-379
Handle: RePEc:cwl:cwldpp:1474
Note: CFP 1157.
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Order Information: Postal: Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA

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