Self-normalized limit theorems for linear processes generated by ρ-mixing innovations

被引：3

作者：

Choi, Yong-Kab ^{[1
]}

Sung, Soo Hak ^{[2
]}

Moon, Hee-Jin ^{[1
]}

机构：

[1] Gyeongsang Natl Univ, Dept Math, Jinju 660701, South Korea

[2] Pai Chai Univ, Dept Appl Math, Taejon 302735, South Korea

来源：

LITHUANIAN MATHEMATICAL JOURNAL | 2017年 / 57卷 / 01期

关键词：

linear process; AR(1) process; central limit theorem; functional central limit theorem; almost sure central limit theorem; self-normalized sum; rho-mixing; INFINITE VARIANCE; RANDOM-VARIABLES; INVARIANCE-PRINCIPLE; SEQUENCES; SUMS;

D O I：

10.1007/s10986-017-9340-9

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we study the asymptotic behavior of the self-normalizer V-n(2) for partial sums of linear processes generated by strictly stationary rho-mixing innovations with infinite variance. Further, by using this we derive self-normalized versions of the CLT, the functional CLT, and the almost sure CLT for partial sums of the processes.

引用

页码：13 / 29

页数：17

共 21 条

[1] WEAK INVARIANCE PRINCIPLE FOR MIXING SEQUENCES IN THE DOMAIN OF ATTRACTION OF NORMAL LAW [J].

Balan, Raluca M. ;

Kulik, Rafal .

STUDIA SCIENTIARUM MATHEMATICARUM HUNGARICA, 2009, 46 (03) :329-343

[2] A universal result in almost sure central limit theory [J].

Berkes, I ;

Csáki, E .

STOCHASTIC PROCESSES AND THEIR APPLICATIONS, 2001, 94 (01) :105-134

[3] Results and problems related to the pointwise central limit theorem [J].

Berkes, I .

ASYMPTOTIC METHODS IN PROBABILITY AND STATISTICS: A VOLUME IN HONOUR OF MIKLOS CSORGO, 1998, :59-96

[4]

Bingham NH., 1989, REGULAR VARIATION

[5] A CENTRAL LIMIT-THEOREM FOR STATIONARY RHO-MIXING SEQUENCES WITH INFINITE VARIANCE [J].

BRADLEY, RC .

ANNALS OF PROBABILITY, 1988, 16 (01) :313-332

[6]

Brockwell PJ., 1991, TIME SERIES THEORY M

[7] AN ALMOST EVERYWHERE CENTRAL LIMIT-THEOREM [J].

BROSAMLER, GA .

MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, 1988, 104 :561-574

[8]

de La Pena V.H., 2009, LIMIT THEORY STAT AP

[9]

Juodis M., 2005, LITH MATH J, V45, P142

[10] A central limit theorem for self-normalized sums of a linear process [J].

Juodis, Mindaugas ;

Rackauskas, Alfredas .

STATISTICS & PROBABILITY LETTERS, 2007, 77 (15) :1535-1541

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