Concentration inequalities for high-dimensional linear processes with dependent innovations

Eduardo Fonseca Mendes; Fellipe Lopes

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arXiv · 2307.12395

Concentration inequalities for high-dimensional linear processes with dependent innovations

Eduardo Fonseca Mendes·Fellipe Lopes

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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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Eduardo Fonseca Mendes, Fellipe Lopes. 2023-07-23. Concentration inequalities for high-dimensional linear processes with dependent innovations. https://arxiv.org/abs/2307.12395

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