Sparse High-Dimensional Vector Autoregressive Bootstrap

TL;DR

This paper presents a high-dimensional bootstrap method for time series that uses sparse VAR models to accurately estimate dependence, providing consistent inference under various error moment conditions.

Contribution

It introduces a novel multiplier bootstrap approach for high-dimensional time series based on sparse VAR models, with proven consistency under different error assumptions.

Findings

Proves bootstrap consistency for high-dimensional means.

Derives a Gaussian approximation for linear process maxima.

Applicable under sub-gaussian and finite moment error conditions.

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.