A Necessary Moment Condition for the Fractional Central Limit Theorem
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A Necessary Moment Condition for the Fractional Central Limit Theorem. / Johansen, Søren; Nielsen, Morten.
In: Econometric Theory, No. 28, 2012, p. 671-679 .Research output: Contribution to journal › Journal article › Research › peer-review
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TY - JOUR
T1 - A Necessary Moment Condition for the Fractional Central Limit Theorem
AU - Johansen, Søren
AU - Nielsen, Morten
PY - 2012
Y1 - 2012
N2 - We discuss the moment condition for the fractional functional central limit theorem (FCLT) for partial sums of x(t)=¿^{-d}u(t) , where -1/21/(d+1/2) 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 when -1/21/(d+1/2) moments are necessary for more general fractional processes. Davidson and de Jong (2000, Econometric Theory 16, 643-- 666) presented a fractional FCLT where onlyq>2 finite moments are assumed. As a corollary to our main theorem we show that their moment condition is not sufficient and hence that their result is incorrect.
AB - We discuss the moment condition for the fractional functional central limit theorem (FCLT) for partial sums of x(t)=¿^{-d}u(t) , where -1/21/(d+1/2) 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 when -1/21/(d+1/2) moments are necessary for more general fractional processes. Davidson and de Jong (2000, Econometric Theory 16, 643-- 666) presented a fractional FCLT where onlyq>2 finite moments are assumed. As a corollary to our main theorem we show that their moment condition is not sufficient and hence that their result is incorrect.
U2 - 10.1017/S0266466611000697
DO - 10.1017/S0266466611000697
M3 - Journal article
SP - 671
EP - 679
JO - Econometric Theory
JF - Econometric Theory
SN - 0266-4666
IS - 28
ER -
ID: 38043678