Berry-Ess\'een Bounds for Long Memory Moving Averages via Stein's Method and Malliavin Calculus

TL;DR

This paper establishes Berry-Esséen bounds for long memory moving averages by applying Stein's method on Wiener chaos, advancing the understanding of their convergence rates.

Contribution

It introduces a novel approach combining Stein's method and Malliavin calculus to derive bounds for long memory processes.

Findings

Derived explicit Berry-Esséen bounds for long memory moving averages.

Extended Stein's method to handle long-range dependence.

Provided theoretical convergence rates for these processes.

Abstract

Using the Stein method on Wiener chaos introduced by Nourdin and Peccati we prove Berry-Ess\'een bounds for long memory moving averages.