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

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  • Liu, Hui
  • Xiong, Yudan
  • Xu, Fangjun

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.

Suggested Citation

  • Liu, Hui & Xiong, Yudan & Xu, Fangjun, 2024. "Limit theorems for functionals of long memory linear processes with infinite variance," Stochastic Processes and their Applications, Elsevier, vol. 167(C).
    • Handle: RePEc:eee:spapps:v:167:y:2024:i:c:s0304414923002090
    DOI: 10.1016/j.spa.2023.104237
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    References listed on IDEAS

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    1. Hailin Sang & Yongli Sang & Fangjun Xu, 2018. "Kernel Entropy Estimation for Linear Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 39(4), pages 563-591, July.
    2. Raluca Balan & Adam Jakubowski & Sana Louhichi, 2016. "Functional Convergence of Linear Processes with Heavy-Tailed Innovations," Journal of Theoretical Probability, Springer, vol. 29(2), pages 491-526, June.
    3. Koul, Hira L. & Surgailis, Donatas, 2001. "Asymptotics of empirical processes of long memory moving averages with infinite variance," Stochastic Processes and their Applications, Elsevier, vol. 91(2), pages 309-336, February.
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