Lithuanian Mathematical Journal

, Volume 57, Issue 1, pp 13–29 | Cite as

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

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Abstract

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 ρ-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.

Keywords

linear process AR(1) process central limit theorem functional central limit theorem almost sure central limit theorem self-normalized sum ρ-mixing 

MSC

60F05 60F17 

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Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  1. 1.Department of MathematicsGyeongsang National UniversityJinjuSouth Korea
  2. 2.Department of Applied MathematicsPai Chai UniversityTaejonSouth Korea

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