In this paper we develop inference for high dimensional linear models, with serially correlated errors. We examine Lasso under the assumption of strong mixing in the covariates and error process, allowing for fatter tails in their distribution. While the Lasso estimator performs poorly under such circumstances, we estimate via GLS Lasso the parameters of interest and extend the asymptotic properties of the Lasso under more general conditions. Our theoretical results indicate that the non-asymptotic bounds for stationary dependent processes are sharper, while the rate of Lasso under general conditions appears slower as $T,p\to \infty$. Further we employ the debiased Lasso to perform inference uniformly on the parameters of interest. Monte Carlo results support the proposed estimator, as it has significant efficiency gains over traditional methods.

翻译：本文针对序列相关误差下的高维线性模型发展了统计推断方法。我们研究在协变量和误差过程满足强混合条件、允许其分布具有厚尾特性时的Lasso估计。鉴于标准Lasso估计量在此类情形下表现不佳，我们通过GLS Lasso估计感兴趣参数，并在更一般条件下拓展了Lasso的渐近性质。理论结果表明，平稳相依过程的非渐近界更为紧凑，而当$T,p\to \infty$时，一般条件下Lasso的收敛速率趋缓。进一步地，我们采用去偏Lasso对感兴趣参数进行一致性推断。蒙特卡洛模拟结果验证了所提估计量的有效性——相较于传统方法，该估计量具有显著的效率提升。