A limit theorem for moving averages in the \alpha -stable domain of attraction

TL;DR

This paper proves a functional limit theorem for regularly varying moving average processes with less restrictive coefficient conditions in the lpha-stable domain of attraction, extending earlier results by Avram and Taqqu.

Contribution

It provides a proof confirming the conjecture that the limit theorem holds under weaker coefficient assumptions in a different topology.

Findings

Established the functional limit theorem under less restrictive conditions

Extended the class of moving average processes satisfying the limit theorem

Confirmed the conjecture posed by Avram and Taqqu

Abstract

In the early 1990's, Avram and Taqqu showed that regularly varying moving average processes with all coefficients nonnegative and the tail index strictly between 0 and 2 satisfy functional limit theorem. They also conjectured that an equivalent statement holds under a certain less restrictive assumption on the coefficients, but in a different topology on the space of c\'adl\'ag functions. We give a proof of this result.