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.

I: Econometric Theory, Nr. 28, 2012, s. 671-679 .

Publikation: Bidrag til tidsskriftTidsskriftartikelfagfællebedømt

Harvard

Johansen, S & Nielsen, M 2012, 'A Necessary Moment Condition for the Fractional Central Limit Theorem', Econometric Theory, nr. 28, s. 671-679 . https://doi.org/10.1017/S0266466611000697

APA

Johansen, S., & Nielsen, M. (2012). A Necessary Moment Condition for the Fractional Central Limit Theorem. Econometric Theory, (28), 671-679 . https://doi.org/10.1017/S0266466611000697

Vancouver

Johansen S, Nielsen M. A Necessary Moment Condition for the Fractional Central Limit Theorem. Econometric Theory. 2012;(28):671-679 . https://doi.org/10.1017/S0266466611000697

Author

Johansen, Søren ; Nielsen, Morten. / A Necessary Moment Condition for the Fractional Central Limit Theorem. I: Econometric Theory. 2012 ; Nr. 28. s. 671-679 .

Bibtex

@article{745449d3646a4cf7b15ef76e980861d7,
title = "A Necessary Moment Condition for the Fractional Central Limit Theorem",
abstract = "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. ",
author = "S{\o}ren Johansen and Morten Nielsen",
year = "2012",
doi = "10.1017/S0266466611000697",
language = "English",
pages = "671--679 ",
journal = "Econometric Theory",
issn = "0266-4666",
publisher = "Cambridge University Press",
number = "28",

}

RIS

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