A functional limit theorem for self-normalized linear processes with random coefficients and i.i.d. heavy-tailed innovations

TL;DR

This paper establishes a self-normalized functional limit theorem for stationary linear processes with heavy-tailed innovations and random coefficients, demonstrating convergence in the Skorokhod M2 topology.

Contribution

It introduces a new limit theorem for such processes under specific boundedness conditions on partial sums of coefficients.

Findings

Proves convergence in the space of càdlàg functions with M2 topology.

Applicable to processes with heavy-tailed innovations and random coefficients.

Provides a theoretical foundation for analyzing such linear processes.

Abstract

In this article we derive a self-normalized functional limit theorem for strictly stationary linear processes with i.i.d. heavy-tailed innovations and random coefficients under the condition that all partial sums of the series of coefficients are a.s. bounded between zero and the sum of the series. The convergence takes part in the space of c\`{a}dl\`{a}g functions on $[0,1]$ with the Skorokhod $M_{2}$ topology.