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

Hui Liu, Yudan Xiong and Fangjun Xu

Stochastic Processes and their Applications, 2024, vol. 167, issue C

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: Linear process; Long memory; Domain of attraction of stable law; Limit theorem (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1016/j.spa.2023.104237

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