Random central limit theorems for linear processes with weakly dependent innovations

Eunju Hwang; Dong Wan Shin

doi:10.1016/j.jkss.2011.10.004

Random central limit theorems for linear processes with weakly dependent innovations

Eunju Hwang, Dong Wan Shin

Department of Statistics

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

Abstract

Random central limit theorems (CLTs) are established for a linear process driven by a strictly stationary ψ-weakly dependent process as well as for the ψ-weakly dependent process itself, whose dependence structure was introduced by Doukhan and Louhichi [Doukhan, P., & Louhichi, S. (1999). A new weak dependence condition and applications to moment inequalities. Stochastic Processes and their Applications, 30 84, 313-342] to generalize mixings and other dependence. Random CLTs are established for partial sums and sample autocovariances of the ψ-weakly dependent process and the linear process under absolute summability.

Original language	English
Pages (from-to)	313-322
Number of pages	10
Journal	Journal of the Korean Statistical Society
Volume	41
Issue number	3
DOIs	https://doi.org/10.1016/j.jkss.2011.10.004
State	Published - Sep 2012

Bibliographical note

Funding Information:
The authors are very grateful for constructive and valuable comments of two anonymous referees. This work was supported partly by the Priority Research Centers Program ( 2009-0093827 ), and partly by the Basic Research Program ( 2010-0023000 ) through the National Research Foundation of Korea (NRF) funded by the Ministry of Education Science and Technology.

Keywords

Linear process
Random central limit theorem
Sample covariance
Weak dependence

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10.1016/j.jkss.2011.10.004

Cite this

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title = "Random central limit theorems for linear processes with weakly dependent innovations",

abstract = "Random central limit theorems (CLTs) are established for a linear process driven by a strictly stationary ψ-weakly dependent process as well as for the ψ-weakly dependent process itself, whose dependence structure was introduced by Doukhan and Louhichi [Doukhan, P., & Louhichi, S. (1999). A new weak dependence condition and applications to moment inequalities. Stochastic Processes and their Applications, 30 84, 313-342] to generalize mixings and other dependence. Random CLTs are established for partial sums and sample autocovariances of the ψ-weakly dependent process and the linear process under absolute summability.",

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author = "Eunju Hwang and Shin, {Dong Wan}",

note = "Funding Information: The authors are very grateful for constructive and valuable comments of two anonymous referees. This work was supported partly by the Priority Research Centers Program ( 2009-0093827 ), and partly by the Basic Research Program ( 2010-0023000 ) through the National Research Foundation of Korea (NRF) funded by the Ministry of Education Science and Technology.",

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AU - Shin, Dong Wan

N1 - Funding Information: The authors are very grateful for constructive and valuable comments of two anonymous referees. This work was supported partly by the Priority Research Centers Program ( 2009-0093827 ), and partly by the Basic Research Program ( 2010-0023000 ) through the National Research Foundation of Korea (NRF) funded by the Ministry of Education Science and Technology.

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N2 - Random central limit theorems (CLTs) are established for a linear process driven by a strictly stationary ψ-weakly dependent process as well as for the ψ-weakly dependent process itself, whose dependence structure was introduced by Doukhan and Louhichi [Doukhan, P., & Louhichi, S. (1999). A new weak dependence condition and applications to moment inequalities. Stochastic Processes and their Applications, 30 84, 313-342] to generalize mixings and other dependence. Random CLTs are established for partial sums and sample autocovariances of the ψ-weakly dependent process and the linear process under absolute summability.

AB - Random central limit theorems (CLTs) are established for a linear process driven by a strictly stationary ψ-weakly dependent process as well as for the ψ-weakly dependent process itself, whose dependence structure was introduced by Doukhan and Louhichi [Doukhan, P., & Louhichi, S. (1999). A new weak dependence condition and applications to moment inequalities. Stochastic Processes and their Applications, 30 84, 313-342] to generalize mixings and other dependence. Random CLTs are established for partial sums and sample autocovariances of the ψ-weakly dependent process and the linear process under absolute summability.

KW - Linear process

KW - Random central limit theorem

KW - Sample covariance

KW - Weak dependence

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JO - Journal of the Korean Statistical Society

JF - Journal of the Korean Statistical Society

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ER -

Random central limit theorems for linear processes with weakly dependent innovations

Abstract

Bibliographical note

Keywords

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