Sparse High-Dimensional Vector Autoregressive Bootstrap

2023-02-02

AI Summary

This paper addresses two key challenges in mean inference for high-dimensional time series: difficulty in modeling temporal dependence structures and weak asymptotic theoretical foundations. We propose a multiplier bootstrap method based on sparse vector autoregression (VAR). We establish, for the first time in high-dimensional time series settings, consistency theory for the sparse VAR-guided bootstrap under two broad distributional assumptions—sub-Gaussian errors and finite absolute moments of order (p > 2). Additionally, we derive a novel Gaussian approximation bound for the maximum of linear processes. The proposed method substantially broadens the applicability of high-dimensional mean inference, ensures uniform consistency of the bootstrap distribution in approximating the true sampling distribution, and enhances both the reliability and robustness of statistical inference.

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.

Problem

• Develops high-dimensional bootstrap for time series
• Ensures consistency under varying error moments
• Derives Gaussian approximation for linear processes

Innovation

• High-dimensional multiplier bootstrap for time series
• Sparsely estimated vector autoregressive model
• Gaussian approximation for maximum mean