Limit theorems for functionals of long memory linear processes with infinite variance (2304.02528v2)

Abstract: Let $X={X_n: n\in\mathbb{N}}$ 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 $\alpha$-stable law with $\alpha\in (0, 2)$. Then, for any integrable and square integrable function $K$ on $\mathbb{R}$, under certain mild conditions, we establish the asymptotic behavior of the partial sum process [ \left{\sum\limits_{n=1}^{[Nt]}\big[K(X_n)-\E K(X_n)\big]:\; t\geq 0\right} ] as $N$ tends to infinity, where $[Nt]$ is the integer part of $Nt$ for $t\geq 0$.