Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/67815 
Year of Publication: 
2010
Series/Report no.: 
Queen's Economics Department Working Paper No. 1244
Publisher: 
Queen's University, Department of Economics, Kingston (Ontario)
Abstract: 
We discuss the moment condition for the fractional functional central limit theorem (FCLT) for partial sums of x_{t}=Delta-d}u_{t}, where d in (-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.
Subjects: 
fractional integration
functional central limit theorem
long memory
moment condition
necessary condition
JEL: 
C22
Document Type: 
Working Paper

Files in This Item:
File
Size
159.65 kB





Items in EconStor are protected by copyright, with all rights reserved, unless otherwise indicated.