Joint functional convergence of partial sums and maxima for moving averages with weakly dependent heavy-tailed innovations and random coefficients

2022/10/24 by Danijel Krizmanić, Krizmanic, Danijel
Decision Sciences · Economics, Econometrics and Finance · Mathematics · #FOS: Mathematics #Probability (math.PR) #Probability and Risk Models #Stochastic processes and financial applications #Stochastic processes and statistical mechanics

paper · pdf · doi:10.48550/arxiv.2210.13275

openalex publication_date 2022/10/24 · openalex created_date 2022/10/31 · openalex updated_date 2026/07/28

Abstract

For moving average processes with random coefficients and heavy-tailed innovations that are weakly dependent in the sense of strong mixing and local dependence condition D' we study joint functional convergence of partial sums and maxima. Under the assumption that all partial sums of the series of coefficients are a.s. bounded between zero and the sum of the series we derive a functional limit theorem in the space of ℝ²-valued càdlàg functions on [0, 1] with the Skorokhod weak M₂ topology.

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