On the rate of approximation in limit theorems for sums of moving averages

We consider a linear process $X_t=\sum_{j=0}^\infty a_j\varepsilon_{t-j}$, $t\ge 1$, where $\varepsilon_i$, $i\in Z$, are independent identically distributed random variables in the domain of attraction of a stable law with index $\alpha$, $0<\alpha\le 2$, $\alpha\ne 1$. Under some conditions on random variables $\varepsilon_i$ and coefficients $a_j$, we look for bounds in approximation of distribution of sums $S_n=B_n^{-1}\sum_{t=1}^nX_t$ by an appropriate stable law. The obtained bounds have optimal order with respect to $n$.