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Joint functional convergence of partial sum and maxima for linear processes

For linear processes with independent and identically distributed innovations that are regularly varying with tail index α ∈ (0, 2), we study functional convergence of the joint partial sum and partial maxima processes in the space of R^2-valued cadlag functions on [0, 1]. Under certain assumptions on the coefficients of the linear process, we derive a functional limit theorem with the Skorohod weak M_2 topology, where the limiting process consists of an α-stable Levy process and an extremal process. We also describe the dependence between these two components of the limit.

functional limit theorem ; Skorohod M2 topology ; regular variation ; linear process ; partial sum and maxima processes

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