A necessary moment condition for the fractional functional central limit theorem

Soren Johansen and Morten Nielsen

CREATES Research Papers from Department of Economics and Business Economics, Aarhus University

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.

Keywords: Fractional integration; functional central limit theorem; long memory; moment condition; necessary condition. (search for similar items in EconPapers)
JEL-codes: C22 (search for similar items in EconPapers)
Pages: 8
Date: 2010
New Economics Papers: this item is included in nep-ets
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
https://repec.econ.au.dk/repec/creates/rp/10/rp10_70.pdf (application/pdf)

Related works:
Journal Article: A NECESSARY MOMENT CONDITION FOR THE FRACTIONAL FUNCTIONAL CENTRAL LIMIT THEOREM (2012)
Working Paper: A Necessary Moment Condition for the Fractional Functional Central Limit Theorem (2010)
Working Paper: A Necessary Moment Condition For The Fractional Functional Central Limit Theorem (2010)
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: https://EconPapers.repec.org/RePEc:aah:create:2010-70

Access Statistics for this paper

More papers in CREATES Research Papers from Department of Economics and Business Economics, Aarhus University
Bibliographic data for series maintained by (bhoejklint@econ.au.dk).