Expansions For The Distribution Of The Maximum Likelihood Estimator Of The Fractional Difference Parameter
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.Download Info
If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.Bibliographic Info
Article provided by Cambridge University Press in its journal Econometric Theory.
Volume (Year): 20 (2004)
Issue (Month): 03 (June)
Pages: 464-484
Contact details of provider:
Postal: The Edinburgh Building, Shaftesbury Road, Cambridge CB2 2RU UK
Fax: +44 (0)1223 325150
Web page: http://journals.cambridge.org/jid_ECTProvider-Email:journals@cambridge.org
Related research
Keywords:References
No references listed on IDEASYou can help add them by filling out this form.
Citations
Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.Cited by:
- Lieberman, Offer & Phillips, Peter C.B., 2008.
"A complete asymptotic series for the autocovariance function of a long memory process,"
Journal of Econometrics,
Elsevier, vol. 147(1), pages 99-103, November.
- Offer Lieberman & Peter C.B. Phillips, 2006. "A Complete Asymptotic Series for the Autocovariance Function of a Long Memory Process," Cowles Foundation Discussion Papers 1586, Cowles Foundation for Research in Economics, Yale University.
- Morten Ørregaard Nielsen & Per Frederiksen, 2005.
"Finite Sample Comparison of Parametric, Semiparametric, and Wavelet Estimators of Fractional Integration,"
Working Papers
1189, Queen's University, Department of Economics.
- Morten �rregaard Nielsen & Per Houmann Frederiksen, 2005. "Finite Sample Comparison of Parametric, Semiparametric, and Wavelet Estimators of Fractional Integration," Econometric Reviews, Taylor and Francis Journals, vol. 24(4), pages 405-443.
- Andrews, Donald W.K. & Lieberman, Offer & Marmer, Vadim, 2006.
"Higher-order improvements of the parametric bootstrap for long-memory Gaussian processes,"
Journal of Econometrics,
Elsevier, vol. 133(2), pages 673-702, August.
- Donald W.K. Andrews & Offer Lieberman, 2002. "Higher-order Improvements of the Parametric Bootstrap for Long-memory Gaussian Processes," Cowles Foundation Discussion Papers 1378, Cowles Foundation for Research in Economics, Yale University.
- D. S. Poskitt, 2006.
"Properties of the Sieve Bootstrap for Fractionally Integrated and Non-Invertible Processes,"
Monash Econometrics and Business Statistics Working Papers
12/06, Monash University, Department of Econometrics and Business Statistics.
- D. S. Poskitt, 2008. "Properties of the Sieve Bootstrap for Fractionally Integrated and Non-Invertible Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 29(2), pages 224-250, 03.
- Offer Lieberman & Peter Phillips, 2008.
"Refined Inference on Long Memory in Realized Volatility,"
Econometric Reviews,
Taylor and Francis Journals, vol. 27(1-3), pages 254-267.
- Offer Lieberman & Peter C. B. Phillips, 2006. "Refined Inference on Long Memory in Realized Volatility," Cowles Foundation Discussion Papers 1549, Cowles Foundation for Research in Economics, Yale University.
- D.S. Poskitt & Simone D. Grose & Gael M. Martin, 2012. "Higher Order Improvements of the Sieve Bootstrap for Fractionally Integrated Processes," Monash Econometrics and Business Statistics Working Papers 9/12, Monash University, Department of Econometrics and Business Statistics.
Lists
This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.Statistics
Access and download statisticsCorrections
When requesting a correction, please mention this item's handle: RePEc:cup:etheor:v:20:y:2004:i:03:p:464-484_20For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Keith Waters).
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.

