Concentration inequalities for high-dimensional linear processes with dependent innovations

• URL: http://arxiv.org/abs/2307.12395v2
• Date: Thu, 17 Oct 2024 15:31:22 GMT
• Title: Concentration inequalities for high-dimensional linear processes with dependent innovations
• Authors: Eduardo Fonseca Mendes, Fellipe Lopes,
• Abstract summary: We develop concentration inequalities for the $l_infty$ norm of vector linear processes with sub-Weibull, mixingale innovations. We apply these inequalities to sparse estimation of large-dimensional VAR(p) systems and heterocedasticity and autocorrelation consistent (HAC) high-dimensional covariance estimation.
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• 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.

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