Time series regression models are commonly used in time series analysis. However, in modern real-world applications, serially correlated data with an ultra-high dimension and fat tails are prevalent. This presents a challenge in developing new statistical tools for time series analysis. In this paper, we propose a novel Bernstein-type inequality for high-dimensional linear processes and apply it to investigate two high-dimensional robust estimation problems: (1) time series regression with fat-tailed and correlated covariates and errors, and (2) fat-tailed vector autoregression. Our proposed approach allows for exponential increases in dimension with sample size under mild moment and dependence conditions, while ensuring consistency in the estimation process.

翻译：一种适用于高维线性过程的Bernstein型不等式及其在时间序列回归鲁棒估计中的应用 Translated Abstract: 时间序列回归模型广泛应用于时间序列分析中。然而，在现代实际应用中，具有超高维度和厚尾特征的序列相关数据非常普遍，这对于开发时间序列分析的新统计工具提出了挑战。本文提出了一种适用于高维线性过程的Bernstein型不等式，并将其应用于研究两个高维鲁棒估计问题：（1）具有厚尾和相关协变量和误差的时间序列回归，（2）具有厚尾的向量自回归。我们的方法可以在轻微的时刻和依赖条件下呈指数增长，同时确保估计过程的一致性。