  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.
