Sparse High-Dimensional Vector Autoregressive Bootstrap

Robert Adámek; Stephan Smeekes; Ines Wilms

Sparse High-Dimensional Vector Autoregressive Bootstrap

Robert Adámek^*, Stephan Smeekes, Ines Wilms

^*Corresponding author for this work

Research output: Working paper / Preprint › Preprint

Abstract

We introduce a high-dimensional multiplier bootstrap for time series data based capturing dependence through a sparsely estimated vector autoregressive model. We prove its consistency for inference on high-dimensional means under two different moment assumptions on the errors, namely sub-gaussian moments and a finite number of absolute moments. In establishing these results, we derive a Gaussian approximation for the maximum mean of a linear process, which may be of independent interest.

Original language	English
Publisher	Cornell University - arXiv
Number of pages	44
Publication status	Published - 2 Feb 2023

Publication series

Series	arXiv.org
Number	2302.01233
ISSN	2331-8422

Keywords

High-dimensional data
Time series
Bootstrap
vector autoregression
linear process

Access to Document

https://arxiv.org/abs/2302.01233Licence: CC BY

Cite this

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title = "Sparse High-Dimensional Vector Autoregressive Bootstrap",

abstract = "We introduce a high-dimensional multiplier bootstrap for time series data based capturing dependence through a sparsely estimated vector autoregressive model. We prove its consistency for inference on high-dimensional means under two different moment assumptions on the errors, namely sub-gaussian moments and a finite number of absolute moments. In establishing these results, we derive a Gaussian approximation for the maximum mean of a linear process, which may be of independent interest.",

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AB - We introduce a high-dimensional multiplier bootstrap for time series data based capturing dependence through a sparsely estimated vector autoregressive model. We prove its consistency for inference on high-dimensional means under two different moment assumptions on the errors, namely sub-gaussian moments and a finite number of absolute moments. In establishing these results, we derive a Gaussian approximation for the maximum mean of a linear process, which may be of independent interest.

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KW - vector autoregression

KW - linear process

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