On mean central limit theorems for stationary sequences

TL;DR

This paper provides estimates of the minimal ${ m L}^1$ distance between the distribution of normalized partial sums and the Gaussian limit for stationary sequences under projective or weak dependence conditions.

Contribution

It introduces new bounds for the convergence rate in the central limit theorem for stationary sequences with dependence structures.

Findings

Derived explicit ${ m L}^1$ distance bounds

Applicable to sequences satisfying Gordin-type conditions

Enhances understanding of convergence rates in dependent sequences

Abstract

In this paper, we give estimates of the minimal ${\mathbb{L}}^1$ distance between the distribution of the normalized partial sum and the limiting Gaussian distribution for stationary sequences satisfying projective criteria in the style of Gordin or weak dependence conditions.