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.

翻译：我们提出了一种针对时间序列数据的高维乘子自助法，该方法通过稀疏估计的向量自回归模型捕捉依赖关系。在关于误差项的两种不同矩假设下（即次高斯矩和有限绝对矩），我们证明了该方法在高维均值推断中的一致性。在建立这些结果的过程中，我们推导了线性过程最大均值的高斯近似，该结果可能具有独立的研究价值。