Maxima of linear processes with heavy-tailed innovations and random coefficients

We investigate maxima of linear processes with i.i.d. heavy-tailed innovations and random coefficients. Using the point process approach we derive functional convergence of the partial maxima stochastic process in the space of non-decreasing c\`{a}dl\`{a}g functions on $[0,1]$ with the Skorohod $M_{1}$ topology.