Joint functional convergence of partial sum and maxima for linear processes

2017/10/21 by Danijel Krizmanić, Krizmanic, Danijel
Mathematics · #Approximation Theory and Sequence Spaces #FOS: Mathematics #Mathematical Approximation and Integration #Probability (math.PR) #Statistical and numerical algorithms

paper · pdf · doi:10.48550/arxiv.1710.07788

openalex publication_date 2017/10/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For linear processes with independent 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. 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 ℝ²--valued càdlàg functions on [0, 1] with the Skorohod weak M₂ topology. Also a joint convergence in the M₂ topology on the first coordinate and in the M₁ topology on the second coordinate is obtained.

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