Concentration inequalities for high-dimensional linear processes with dependent innovations

Abstract

We develop concentration inequalities for the l_ 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.

Tasks

Reproductions