  In this paper, we establish a joint (bivariate) functional central limit
theorem of the sample quantile and the $r$-th absolute centred sample moment
for functionals of mixing processes. More precisely, we consider $L_2$-near
epoch dependent processes that are functionals of either $\phi$-mixing or
absolutely regular processes. The general results we obtain can be used for two
classes of popular and important processes in applications: The class of
augmented GARCH($p$,$q$) processes with independent and identically distributed
innovations (including many GARCH variations used in practice) and the class of
ARMA($p$,$q$) processes with mixing innovations (including, e.g., ARMA-GARCH
processes). For selected examples, we provide exact conditions on the moments
and parameters of the process for the joint asymptotics to hold.
