  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.
