Moderate deviations on different scales: no relations

TL;DR

This paper presents an example of a discrete-time stationary random process where sums follow a normal approximation within certain moderate deviation regions but deviate outside those regions.

Contribution

It provides a counterexample illustrating the limits of normal approximation in moderate deviations for stationary processes.

Findings

Normal approximation holds in specific moderate deviation regions

Deviations occur outside these regions

Highlights limitations of existing approximation methods

Abstract

An example of a discrete-time stationary random process whose sums follow the normal approximation within a given part of the region of moderate deviations, but violate it outside this part.