A Necessary Moment Condition for the Fractional Functional Central Limit Theorem
We 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.
|Date of creation:||Oct 2010|
|Date of revision:|
|Contact details of provider:|| Postal: |
Phone: (+45) 35 32 30 10
Fax: +45 35 32 30 00
Web page: http://www.econ.ku.dk
More information through EDIRC
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.
When requesting a correction, please mention this item's handle: RePEc:kud:kuiedp:1029. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Thomas Hoffmann)
If references are entirely missing, you can add them using this form.