A Bernstein type inequality and moderate deviations for weakly dependent sequences

TL;DR

This paper establishes a Bernstein-type tail inequality for weakly dependent sequences, including mixing and Markov chains, and applies it to derive moderate deviation results for various stochastic models.

Contribution

Introduces a novel tail inequality for unbounded weakly dependent sequences and derives moderate deviations, extending existing results to broader classes of stochastic processes.

Findings

Tail inequality for maximum of partial sums of weakly dependent sequences

Asymptotic moderate deviations for Markov chains and linear process functions

Applicable to ARCH models and other dependent stochastic processes

Abstract

In this paper we present a tail inequality for the maximum of partial sums of a weakly dependent sequence of random variables that are not necessarily bounded. The class considered includes geometrically and subgeometrically strongly mixing sequences. The result is then used to derive asymptotic moderate deviations results. Applications include classes of Markov chains, functions of linear processes with absolutely regular innovations and ARCH models