Deviation inequalities for sums of weakly dependent time series

TL;DR

This paper develops new Bernstein-type deviation inequalities for sums of weakly dependent time series, analyzing the impact of dependence and providing examples where these inequalities apply.

Contribution

It introduces novel deviation inequalities for weakly dependent time series, extending classical results to non-mixing dynamical systems and Bernoulli shifts.

Findings

Deviation inequalities hold for certain non-mixing systems

The inequalities quantify the effect of weak dependence

Proofs utilize blocks technique and coupling arguments

Abstract

In this paper we give new deviation inequalities of Bernstein's type for the partial sums of weakly dependent time series. The loss from the independent case is studied carefully. We give non mixing examples such that dynamical systems and Bernoulli shifts for whom our deviation inequalities hold. The proofs are based on the blocks technique and different coupling arguments.