# Cram\'{e}r type moderate deviations for stationary sequences of bounded random variables

## TL;DR

This paper establishes Cramér type moderate deviation results for stationary bounded sequences, providing theoretical tools for probabilistic bounds and applications in various dependent processes.

## Contribution

It introduces new Cramér type moderate deviation results for stationary sequences of bounded variables, extending existing probabilistic bounds to dependent data.

## Key findings

- Derives Cramér type moderate deviations for stationary sequences
- Implements results to quantile coupling inequalities and mixing sequences
- Provides Berry-Esseen bounds for dependent processes

## Abstract

We derive Cram\'{e}r type moderate deviations for stationary sequences of bounded random variables. Our results imply the moderate deviation principles and a Berry-Esseen bound. Applications to quantile coupling inequalities, functions of $\phi$-mixing sequences, and contracting Markov chains are discussed.