Expansions for the distribution of the maximum likelihood estimator of the fractional difference parameter

Offer Lieberman, Peter C.B. Phillips

Research output: Contribution to journalArticlepeer-review

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Abstract

The maximum likelihood estimator (MLE) of the fractional difference parameter in the Gaussian ARFIMA(0, d, 0) model is well known to be asymptotically N(0, 6/π 2 ). This paper develops asymptotic expansions to the distribution of this statistic under the assumption of a known unit variance. The correction term for the density is shown to be independent of d, so that the MLE is second-order pivotal for d. This feature of the MLE is unusual, at least in time series contexts. Simulations show that the normal approximation is poor and that the expansions can make a significant improvement in accuracy provided the correction terms are computed without further asymptotic approximation.

Original languageEnglish
Pages (from-to)464-484
Number of pages21
JournalEconometric Theory
Volume20
Issue number3
DOIs
StatePublished - Jun 2004
Externally publishedYes

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