A functional limit theorem for moving averages with weakly dependent heavy-tailed innovations

TL;DR

This paper extends a functional limit theorem for moving averages with heavy-tailed innovations from i.i.d. to weakly dependent innovations, broadening its applicability in stochastic process analysis.

Contribution

It generalizes existing results by establishing a functional limit theorem under weak dependence conditions, specifically strong mixing and local dependence, for moving averages with heavy-tailed innovations.

Findings

Proves convergence in the Skorohod $M_2$ topology for weakly dependent innovations.

Extends previous i.i.d. results to dependent cases under strong mixing.

Provides a broader framework for analyzing heavy-tailed moving averages.

Abstract

Recently a functional limit theorem for sums of moving averages with random coefficients and i.i.d. heavy tailed innovations has been obtained under the assumption that all partial sums of the series of coefficients are a.s. bounded between zero and the sum of the series. The convergence takes place in the space $D[0,1]$ of c\`{a}dl\`{a}g functions with the Skorohod $M_{2}$ topology. In this article we extend this result to the case when the innovations are weakly dependent in the sense of strong mixing and local dependence condition $D'$.