  Recently, for the joint partial sum and partial maxima processes constructed
from linear processes with independent identically distributed innovations that
are regularly varying with tail index $\alpha \in (0, 2)$, a functional limit
theorem with the Skorohod weak $M_{2}$ topology has been obtained. In this
paper we show that, if all the coefficients of the linear processes are of the
same sign, the functional convergence holds in the stronger topology, i.e. in
the Skorohod weak $M_{1}$ topology on the space of $\mathbb{R}^{2}$--valued
c\`{a}dl\`{a}g functions on $[0, 1]$.
