The principle of invariance in the Donsker form to the partial sum processes of finite order moving averages

TL;DR

This paper investigates the invariance principle for partial sums of finite-order moving averages with regularly varying memory functions, establishing Gaussian approximation conditions for convergence in the Donsker form.

Contribution

It provides new sufficient conditions for the invariance principle in the Donsker form for finite-order moving averages with regularly varying memory functions.

Findings

Established Gaussian approximation conditions for the partial sum process.

Proved $C$-convergence in the invariance principle.

Extended the invariance principle to processes with regularly varying variance functions.

Abstract

We consider the process of partial sums of moving averages of finite order with a regular varying memory function, constructed from a stationary sequence, variance of the sum of which is a regularly varying function. We study the Gaussian approximation of this process of partial sums with the aid of a certain class of Gaussian processes, and obtain sufficient conditions for the $C$-convergence in the invariance principle in the Donsker form