  For moving average processes with random coefficients and heavy-tailed
innovations that are weakly dependent in the sense of strong mixing and local
dependence condition $D'$ we study joint functional convergence of partial sums
and maxima. Under the assumption that all partial sums of the series of
coefficients are a.s. bounded between zero and the sum of the series we derive
a functional limit theorem in the space of $\mathbb{R}^{2}$-valued
c\`{a}dl\`{a}g functions on $[0, 1]$ with the Skorokhod weak $M_{2}$ topology.
