  For a strictly stationary sequence of $\mathbb{R}_{+}^{d}$--valued random
vectors we derive functional convergence of partial maxima stochastic processes
under joint regular variation and weak dependence conditions. The limit process
is an extremal process and the convergence takes place in the space of
$\mathbb{R}_{+}^{d}$--valued c\`{a}dl\`{a}g functions on $[0,1]$, with the
Skorohod weak $M_{1}$ topology. We also show that this topology in general can
not be replaced by the stronger (standard) $M_{1}$ topology. The theory is
illustrated on three examples, including the multivariate squared GARCH process
with constant conditional correlations.
