Joint functional convergence of partial sums and maxima for linear processes*

Abstract

For linear processes with independent identically distributed innovations that are regularly varying with tail index α ∈ (0, 2), we study the 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 in the space of ℝ2-valued cadlag functions on [0, 1] with the Skorokhod weak M2 topology.We also obtain a joint convergence in the M2 topology on the first coordinate and in theM1 topology on the second coordinate.