Joint functional convergence of partial sum and maxima for linear processes

For linear processes with independent identically distributed innovations that are regularly varying with tail index $\alpha \in (0,2)$, we study functional convergence of the joint partial sum and partial maxima processes. We derive a functional limit theorem under certain assumptions on the coefficients of the linear processes which enable the functional convergence to hold in the space of ${\mathbb{R}}^2$–valued c`adl`ag functions on $[0,1]$ with the Skorohod weak $M_2$ topology. Also a joint convergence in the $M_2$ topology on the first coordinate and in the $M_1$ topology on the second coordinate is obtained.