# A note on linear processes with tapered innovations

## TL;DR

This paper investigates the asymptotic behavior of partial sums of linear processes with innovations that have heavy-tailed tapered distributions, showing they can converge to fractional Brownian motion or linear fractional stable motion depending on tapering.

## Contribution

It introduces a framework for understanding the limit processes of linear processes with tapered heavy-tailed innovations, depending on the tapering parameter and filter properties.

## Key findings

- Limit process can be fractional Brownian motion or linear fractional stable motion.
- The type of limit depends on the tapering parameter and filter characteristics.
- Provides conditions under which different limit processes arise.

## Abstract

In the paper we consider the partial sum process $\sum_{k=1}^{[nt]}X_k^{(n)}$, where $\{X_k^{(n)}, \ k\in Z\},\ n\ge 1,$ is a series of linear processes with innovations having heavy-tailed tapered distributions with tapering parameter $b_n$ depending on $n$. It is shown that, depending on the properties of a filter of a linear process under consideration and on the parameter $b_n$ defining if the tapering is hard or soft, the limit process for such partial sum process can be fractional Brownian motion or linear fractional stable motion.