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Sparse High-Dimensional Vector Autoregressive Bootstrap
Robert Adamek, Stephan Smeekes, Ines Wilms · 2023-02-03 · via stat updates on arXiv.org

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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