Joint functional convergence of partial sums and maxima for linear processes*
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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 càdlàg 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.
Keywordsextremal process functional limit theorem linear process regular variation Skorokhod M2 topology stable Lévy process
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