The functional central limit theorem for a family of GARCH observations with applications

被引：18

作者：

Berkes, Istvan ^{[1
]}

Hoermann, Siegfried ^{[2
]}

Horvath, Lajos ^{[2
]}

机构：

[1] Graz Univ Technol, Inst Stat, A-8010 Graz, Austria

[2] Univ Utah, Dept Math, Salt Lake City, UT 84112 USA

来源：

STATISTICS & PROBABILITY LETTERS | 2008年 / 78卷 / 16期

关键词：

D O I：

10.1016/j.spl.2008.03.021

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

We consider polynomial GARCH(p, q) variables which define an important subclass of Duan's augmented GARCH(p, q) processes. We prove functional central limit theorems for the observations as well as for the volatility process under the assumption of finite second moments. The results imply the convergence of CUSUM, MOSUM and Dickey-Fuller Statistics Under optimal conditions. (c) 2008 Elsevier B.V. All rights reserved.

引用

页码：2725 / 2730

页数：6

共 50 条

[31] Functional central limit theorem for subgraph counting processes
Owada, Takashi
ELECTRONIC JOURNAL OF PROBABILITY, 2017, 22
[32] A functional central limit theorem for a class of urn models
Basak, GK
Dasgupta, A
PROCEEDINGS OF THE INDIAN ACADEMY OF SCIENCES-MATHEMATICAL SCIENCES, 2005, 115 (04): : 493 - 498
[33] A FUNCTIONAL CENTRAL-LIMIT-THEOREM IN DIOPHANTINE APPROXIMATION
SAMUR, JD
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1991, 111 (04) : 901 - 911
[34] REMARKS ON THE FUNCTIONAL CENTRAL LIMIT-THEOREM FOR MARTINGALES
GANSSLER, P
HAUSLER, E
ZEITSCHRIFT FUR WAHRSCHEINLICHKEITSTHEORIE UND VERWANDTE GEBIETE, 1979, 50 (03): : 237 - 243
[35] On the functional central limit theorem via martingale approximation
Gordin, Mikhail
Peligrad, Magda
BERNOULLI, 2011, 17 (01) : 424 - 440
[36] A FUNCTIONAL CENTRAL LIMIT THEOREM FOR NEGATIVELY ASSOCIATED SEQUENCE
LU CHUANRONG
AppliedMathematics:AJournalofChineseUniversities(SeriesB), 1997, (04) : 3 - 8
[37] Strong functional version of the central limit theorem for martingales
Chaabane, F
COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE, 1996, 323 (02): : 195 - 198
[38] A functional central limit theorem for a class of urn models
Gopal K. Basak
Amites Dasgupta
Proceedings of the Indian Academy of Sciences - Mathematical Sciences, 2005, 115 : 493 - 498
[39] RANDOM FUNCTIONAL CENTRAL LIMIT-THEOREM FOR MARTINGALES
BABU, GJ
GHOSH, M
ACTA MATHEMATICA ACADEMIAE SCIENTIARUM HUNGARICAE, 1976, 27 (3-4): : 301 - 306
[40] A Functional Central Limit Theorem for Polaron Path Measures
Betz, Volker
Polzer, Steffen
COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 2022, 75 (11) : 2345 - 2392

← 1 2 3 4 5 →