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

TL;DR

This paper establishes a joint functional limit theorem for partial sums and maxima of moving average processes with heavy-tailed, weakly dependent innovations and random coefficients, using the Skorokhod weak M2 topology.

Contribution

It introduces a novel joint convergence result for partial sums and maxima in moving averages with heavy tails and dependence, under specific boundedness conditions on the coefficients.

Findings

Proves joint functional convergence in Skorokhod weak M2 topology.

Extends limit theorems to processes with heavy-tailed, weakly dependent innovations.

Provides conditions on coefficients ensuring bounded partial sums.

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 $\mathbb{R}^{2}$-valued c\`{a}dl\`{a}g functions on $[0, 1]$ with the Skorokhod weak $M_{2}$ topology.