Sparse High-Dimensional Vector Autoregressive Bootstrap

Robert Adamek; Stephan Smeekes; Ines Wilms

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arXiv · 2302.01233

Sparse High-Dimensional Vector Autoregressive Bootstrap

Robert Adamek·Stephan Smeekes·Ines Wilms

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Abstract

We introduce a high-dimensional multiplier bootstrap for time series data based on 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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Robert Adamek, Stephan Smeekes, Ines Wilms. 2023-02-02. Sparse High-Dimensional Vector Autoregressive Bootstrap. https://arxiv.org/abs/2302.01233

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