EXPANSIONS FOR THE DISTRIBUTION OF THE MAXIMUM LIKELIHOOD ESTIMATOR OF THE FRACTIONAL DIFFERENCE PARAMETER

Offer Lieberman and Peter C. B. Phillips ()

Econometric Theory, 2004, vol. 20, issue 03, pages 464-484

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 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.This paper was commenced and revised while Lieberman was visiting the Cowles Foundation during 2000 2002. Lieberman thanks the Cowles Foundation for support and hospitality during this visit. Phillips thanks the NSF for support under grants SBR 97-30295 and SES 0092509.

Date: 2004
View citations in EconPapers

Downloads: (external link)
http://journals.cambridge.org/abstract_S0266466604203024 link to article abstract page (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: http://EconPapers.repec.org/RePEc:cup:etheor:v:20:y:2004:i:03:p:464-484_20

Access Statistics for this article

More articles in Econometric Theory from Cambridge University Press
Address: The Edinburgh Building, Shaftesbury Road, Cambridge CB2 2RU UK
Series data maintained by Mike Eden ().