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：时间序列回归模型常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十分普遍。这对开发新的时间序列分析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伯恩斯坦型新不等式，并将其应用于研究两个高维稳健估计问题：（1）在协变量和误差项存在厚尾及相关性条件下的时间序列回归，以及（2）厚尾向量自回归模型。在较弱的矩条件和相依性条件下，我们的方法允许维度随样本量呈指数级增长，同时确保估计过程的一致性。