Let \(X=\{X_n: n\in {\mathbb {N}}\}\) be a linear process in which the coefficients are of the form \(a_i=i^{-1}\ell (i)\) with \(\ell \) being a slowly varying function at the infinity and the innovations are independent and identically distributed random variables belonging to the domain of attraction of an \(\alpha \) -stable law with \(\alpha \in (1, 2]\) . We will establish the asymptotic behavior of the partial sum process \(\begin{aligned} \bigg \{\sum \limits _{n=1}^{[Nt]} X_n: t\ge 0\bigg \} \end{aligned}\) as N tends to infinity, where [t] is the integer part of the nonnegative number t.
