Concentration inequalities for high-dimensional linear processes with dependent innovations

TL;DR

This paper develops concentration inequalities for high-dimensional linear processes with dependent innovations, enabling improved bounds for covariance estimation and sparse VAR models in complex dependent data settings.

Contribution

It introduces new concentration inequalities for vector linear processes with dependent innovations, applicable to high-dimensional covariance and VAR model estimation.

Findings

Provides bounds for the maximum entrywise norm of autocovariance matrices.

Enables sparse estimation of large-dimensional VAR systems.

Improves covariance estimation under dependence and heteroscedasticity.

Abstract

We develop concentration inequalities for the $l_\infty$ norm of vector linear processes with sub-Weibull, mixingale innovations. This inequality is used to obtain a concentration bound for the maximum entrywise norm of the lag-$h$ autocovariance matrix of linear processes. We apply these inequalities to sparse estimation of large-dimensional VAR(p) systems and heterocedasticity and autocorrelation consistent (HAC) high-dimensional covariance estimation.