Skorokhod $M_1$ convergence of maxima of multivariate linear processes with heavy-tailed innovations and random coefficients

We derive functional convergence of the partial maxima stochastic processes of multivariate linear processes with weakly dependent heavy-tailed innovations and random coefficients. The convergence takes place in the space of ${\mathbb{R}}^d$–valued càdlàg functions on $[0,1]$ endowed with the weak Skorokhod $M_1$ topology. We also show that this topology in general can not be replaced by the standard (or strong) $M_1$ topology.