Skorokhod $M_{1}$ convergence of maxima of multivariate linear processes with heavy-tailed innovations and random coefficients

Abstract

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 c\`{a}dl\`{a}g 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.