High-dimensional time series data appear in many scientific areas in the current data-rich environment. Analysis of such data poses new challenges to data analysts because of not only the complicated dynamic dependence between the series, but also the existence of aberrant observations, such as missing values, contaminated observations, and heavy-tailed distributions. For high-dimensional vector autoregressive (VAR) models, we introduce a unified estimation procedure that is robust to model misspecification, heavy-tailed noise contamination, and conditional heteroscedasticity. The proposed methodology enjoys both statistical optimality and computational efficiency, and can handle many popular high-dimensional models, such as sparse, reduced-rank, banded, and network-structured VAR models. With proper regularization and data truncation, the estimation convergence rates are shown to be nearly optimal under a bounded fourth moment condition. Consistency of the proposed estimators is also established under a relaxed bounded $(2+2\epsilon)$-th moment condition, for some $\epsilon\in(0,1)$, with slower convergence rates associated with $\epsilon$. The efficacy of the proposed estimation methods is demonstrated by simulation and a real example.

翻译：在目前数据丰富的环境中,许多科学领域都出现了高维时间序列数据。对这些数据的分析给数据分析员带来了新的挑战,不仅因为该系列之间复杂的动态依赖性,而且由于存在偏差观测,如缺失值、污染观测和重尾分布等。对于高维矢量自动递减模型,我们引入了一个统一的估算程序,该程序非常有力,可以模拟误差、重尾噪声污染和有条件的超升度。拟议方法既具有统计最佳性,又具有计算效率,并能处理许多受欢迎的高维模型,如稀疏、降级、带宽和网络结构的VAR模型。在适当规范化和数据变速的情况下,估计趋同率在捆绑的第四分钟条件下几乎是最佳的。拟议估算的一致性也是在宽松的约束值为$(2+2\epsilon)-thimtality条件下确立的。对于一些美元(0,1美元),可以处理许多受欢迎的高维维模型,如稀、降级、带带和网络结构的VAR模型。在适当调整和数据变速的情况下,估算汇率与美元和模拟所展示的实际效益是。