Functional convergence for moving averages with heavy tails and random coefficients

TL;DR

This paper establishes the functional convergence of sums of moving averages with random coefficients and heavy-tailed innovations, under certain moment conditions, in the space of cadlag functions with the Skorohod M2 topology.

Contribution

It provides new conditions under which the partial sum processes of such moving averages converge functionally in the Skorohod M2 topology.

Findings

Proves functional convergence in $D[0,1]$ space.

Identifies conditions on coefficients and innovations for convergence.

Extends existing results to heavy-tailed and random coefficient settings.

Abstract

We study functional convergence of sums of moving averages with random coefficients and heavy-tailed innovations. Under some standard moment conditions and the assumption that all partial sums of the series of coefficients are a.s. bounded between zero and the sum of the series we obtain functional convergence of the corresponding partial sum stochastic process in the space $D[0,1]$ of c\`{a}dl\`{a}g functions with the Skorohod $M_{2}$ topology.