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:我们为基于时间序列数据的时间序列数据引入一个高维乘数陷阱,通过一种微小估计的矢量自动递减模型来捕捉依赖性。我们证明,在两种不同的假设下,即在误差的瞬间,即亚加盟时刻和一定数量的绝对时刻,对高维手段的推论是一致的。在确定这些结果时,我们得出一个高斯近似值,以得出线性过程的最大平均值,这可能是独立感兴趣的。