Abstract: Time series regression models are commonly used in time series analysis. However, in modern applications, data are often serially correlated and have an ultrahigh dimension and fat tails, making it difficult to develop new time series analysis tools. 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) a time series regression with fat-tailed and correlated covariates and errors, and (2) a fat-tailed vector autoregression. Our proposed approach allows for exponential increases in the dimension with the sample size, under mild moment and dependence conditions, while ensuring consistency in the estimation process.

Key words and phrases: Bernstein-type inequality, fat-tailed data, high dimensional time series, robust estimation.