High dimensional non-Gaussian time series data are increasingly encountered in a wide range of applications. Conventional estimation methods and technical tools are inadequate when it comes to ultra high dimensional and heavy-tailed data. We investigate robust estimation of high dimensional autoregressive models with fat-tailed innovation vectors by solving a regularized regression problem using convex robust loss function. As a significant improvement, the dimension can be allowed to increase exponentially with the sample size to ensure consistency under very mild moment conditions. To develop the consistency theory, we establish a new Bernstein type inequality for the sum of autoregressive models. Numerical results indicate a good performance of robust estimates.

翻译：在一系列广泛的应用中,人们越来越多地遇到高维非古塞西时间序列数据。常规估算方法和技术工具在超高维和重尾数据方面是不足的。我们调查了高维自动递减模型的强力估算,其中含有高维自动递减创新矢量,通过使用曲线稳健的损失函数解决常规回归问题。作为重大改进,可以允许该维度随样本大小的指数增长,以确保在非常温和的瞬间条件下的一致性。为了发展一致性理论,我们为自动递减模型的总和建立了新的伯恩斯坦型不平等。数字结果表明稳健的估算效果良好。