  We study functional convergence of sums of moving averages with random
coefficients and heavy-tailed innovations. Under some standard moment
conditions and the assumption that all partial sums of the series of
coefficients are a.s. bounded between zero and the sum of the series we obtain
functional convergence of the corresponding partial sum stochastic process in
the space $D[0,1]$ of c\`{a}dl\`{a}g functions with the Skorohod $M_{2}$
topology.
