COWLES FOUNDATION FOR RESEARCH IN
ECONOMICS Box 208281
COWLES FOUNDATION DISCUSSION PAPER NO. 1474 Expansions for Approximate Maximum Likelihood Estimators Offer Lieberman and Peter C.B. Phillips July 2004 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-1ln n) improvement over the delta method. For statistics that are not second-order pivotal, the improvement is generally only of the order o(n-1/2ln n). Keywords: ARFIMA; Bootstrap; Edgeworth expansion; Fractional differencing; Pivotal statistic JEL Classification: C13, C22 |
