Limit theorems for functionals of long memory linear processes with infinite variance

Hui Liu; Yudan Xiong; Fangjun Xu

doi:10.1016/j.spa.2023.104237

Limit theorems for functionals of long memory linear processes with infinite variance

Hui Liu
, Yudan Xiong
, Fangjun Xu^*

^*Corresponding author for this work

School of Statistics

East China Normal University

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

2 Scopus citations

Abstract

Let X={X_n:n∈N} be a long memory linear process in which the coefficients are regularly varying and innovations are independent and identically distributed and belong to the domain of attraction of an α-stable law with α∈(0,2). Then, for any integrable and square integrable function K on R, under certain mild conditions, we establish the asymptotic behavior of the partial sum process ∑n=1[Nt][K(X_n)−EK(X_n)]:t≥0as N tends to infinity, where [Nt] is the integer part of Nt for t≥0.

Original language	English
Article number	104237
Journal	Stochastic Processes and their Applications
Volume	167
DOIs	https://doi.org/10.1016/j.spa.2023.104237
State	Published - Jan 2024

Keywords

Domain of attraction of stable law
Limit theorem
Linear process
Long memory

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10.1016/j.spa.2023.104237

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title = "Limit theorems for functionals of long memory linear processes with infinite variance",

abstract = "Let X=\{Xn:n∈N\} be a long memory linear process in which the coefficients are regularly varying and innovations are independent and identically distributed and belong to the domain of attraction of an α-stable law with α∈(0,2). Then, for any integrable and square integrable function K on R, under certain mild conditions, we establish the asymptotic behavior of the partial sum process ∑n=1[Nt][K(Xn)−EK(Xn)]:t≥0as N tends to infinity, where [Nt] is the integer part of Nt for t≥0.",

keywords = "Domain of attraction of stable law, Limit theorem, Linear process, Long memory",

author = "Hui Liu and Yudan Xiong and Fangjun Xu",

note = "Publisher Copyright: {\textcopyright} 2023 Elsevier B.V.",

year = "2024",

month = jan,

doi = "10.1016/j.spa.2023.104237",

language = "英语",

volume = "167",

journal = "Stochastic Processes and their Applications",

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TY - JOUR

T1 - Limit theorems for functionals of long memory linear processes with infinite variance

AU - Liu, Hui

AU - Xiong, Yudan

AU - Xu, Fangjun

PY - 2024/1

Y1 - 2024/1

N2 - Let X={Xn:n∈N} be a long memory linear process in which the coefficients are regularly varying and innovations are independent and identically distributed and belong to the domain of attraction of an α-stable law with α∈(0,2). Then, for any integrable and square integrable function K on R, under certain mild conditions, we establish the asymptotic behavior of the partial sum process ∑n=1[Nt][K(Xn)−EK(Xn)]:t≥0as N tends to infinity, where [Nt] is the integer part of Nt for t≥0.

AB - Let X={Xn:n∈N} be a long memory linear process in which the coefficients are regularly varying and innovations are independent and identically distributed and belong to the domain of attraction of an α-stable law with α∈(0,2). Then, for any integrable and square integrable function K on R, under certain mild conditions, we establish the asymptotic behavior of the partial sum process ∑n=1[Nt][K(Xn)−EK(Xn)]:t≥0as N tends to infinity, where [Nt] is the integer part of Nt for t≥0.

KW - Domain of attraction of stable law

KW - Limit theorem

KW - Linear process

KW - Long memory

UR - https://www.scopus.com/pages/publications/85174447231

U2 - 10.1016/j.spa.2023.104237

DO - 10.1016/j.spa.2023.104237

M3 - 文章

AN - SCOPUS:85174447231

SN - 0304-4149

VL - 167

JO - Stochastic Processes and their Applications

JF - Stochastic Processes and their Applications

M1 - 104237

ER -

Limit theorems for functionals of long memory linear processes with infinite variance

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Keywords

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