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Concentration inequalities for high-dimensional linear processes with dependent innovations (2307.12395v2)
Published 23 Jul 2023 in math.ST, stat.ME, stat.ML, and stat.TH
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.