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

A Bernstein-type Inequality for High Dimensional Linear Processes with Applications to Robust Estimation of Time Series Regressions