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

In the early 1990s, Avram and Taqqu showed that regularly varying moving average processes with all coefficients nonnegative and the tail index αα strictly between 0 and 2 satisfy the 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 càdlàg functions. We give a proof of this result.