We introduce a high-dimensional multiplier bootstrap for time series data based 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来捕获依赖性。我们在两种不同的误差矩假设下证明了该方法在高维均值推断中的一致性，即次高斯矩和有限绝对矩。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，这本身可能具有独立的研究价值。