A note on linear processes with tapered innovations

In the paper, we consider the partial-sum process ∑k=1ntXkn,\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {\sum}_{k=1}^{\left[ nt\right]}{X}_k^{(n)}, $$\end{document} where Xnnk∈ℤ,n≥1,\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \left\{{X}_n^{(n)},k\in \mathbb{Z}\right\},n\ge 1, $$\end{document} is a series of linear processes with innovations having heavy-tailed tapered distributions with tapering parameter bn depending on n. We show that, depending on the properties of a filter of a linear process under consideration and on the parameter bn defining if the tapering is hard or soft, the limit process for such partial-sum process can be a fractional Brownian motion or linear fractional stable motion.