A note on linear processes with tapered innovations

Abstract

In the paper, we consider the partial-sum process \( {\sum}_{k=1}^{\left[ nt\right]}{X}_k^{(n)}, \) where \( \left\{{X}_n^{(n)},k\in \mathbb{Z}\right\},n\ge 1, \) 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.