A Necessary Moment Condition for the Fractional Functional Central Limit Theorem
AbstractWe discuss the moment condition for the fractional functional central limit theorem (FCLT) for partial sums of x(t)=Δ^(-d)u(t), where d є (-1/2,1/2) is the fractional integration parameter and u(t) is weakly dependent. The classical condition is existence of q>max(2,(d+1/2)-¹) moments of the innovation sequence. When d is close to -1/2 this moment condition is very strong. Our main result is to show that under some relatively weak conditions on u(t), the existence of q≥max(2,(d+1/2)-¹) is in fact necessary for the FCLT for fractionally integrated processes and that q>max(2,(d+1/2)-¹) moments are necessary and sufficient for more general fractional processes. Davidson and de Jong (2000) presented a fractional FCLT where only q>2 finite moments are assumed, which is remarkable because it is the only FCLT where the moment condition has been weakened relative to the earlier condition. As a corollary to our main theorem we show that their moment condition is not sufficient.
Download InfoIf 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 InfoPaper provided by University of Copenhagen. Department of Economics in its series Discussion Papers with number 10-29.
Length: 8 pages
Date of creation: Oct 2010
Date of revision:
Contact details of provider:
Postal: Øster Farimagsgade 5, Building 26, DK-1353 Copenhagen K., Denmark
Phone: (+45) 35 32 30 10
Fax: +45 35 32 30 00
Web page: http://www.econ.ku.dk
More information through EDIRC
fractional integration; functional central limit theorem; long memory; moment condition; necessary condition;
Other versions of this item:
- Johansen, Søren & Ørregaard Nielsen, Morten, 2012. "A Necessary Moment Condition For The Fractional Functional Central Limit Theorem," Econometric Theory, Cambridge University Press, vol. 28(03), pages 671-679, June.
- Søren Johansen & Morten Ørregaard Nielsen, 2010. "A necessary moment condition for the fractional functional central limit theorem," Working Papers 1244, Queen's University, Department of Economics.
- Søren Johansen & Morten Ørregaard Nielsen, 2010. "A necessary moment condition for the fractional functional central limit theorem," CREATES Research Papers 2010-70, School of Economics and Management, University of Aarhus.
- C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models
This paper has been announced in the following NEP Reports:
- NEP-ALL-2010-11-06 (All new papers)
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- de Jong, Robert M. & Davidson, James, 2000.
"The Functional Central Limit Theorem And Weak Convergence To Stochastic Integrals I,"
Cambridge University Press, vol. 16(05), pages 621-642, October.
- Davidson, James & de Jong, Robert M., 2000. "The Functional Central Limit Theorem And Weak Convergence To Stochastic Integrals Ii," Econometric Theory, Cambridge University Press, vol. 16(05), pages 643-666, October.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Sabine Fischer).
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.