Edgeworth expansions for weakly dependent random variables

TL;DR

This paper establishes conditions under which Edgeworth expansions, providing refined approximations to the CLT, hold for weakly dependent variables such as those from dynamical systems and Markov chains, using spectral methods.

Contribution

It introduces spectral techniques to derive Edgeworth expansions for weakly dependent variables, extending classical results to more complex dependent structures.

Findings

Edgeworth expansions exist under certain spectral conditions

Applicable to dynamical systems like piece-wise expanding maps

Valid for strongly ergodic Markov chains

Abstract

We discuss sufficient conditions that guarantee the existence of asymptotic expansions for the Central Limit Theorem for weakly dependent random variables including observations arising from sufficiently chaotic dynamical systems like piece-wise expanding maps, and strongly ergodic Markov chains. We primarily use spectral techniques to obtain the results.