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：本文针对存在序列相关误差的高维线性模型进行推断研究。我们在协变量与误差过程满足强混合假设的条件下分析Lasso方法，允许其分布具有更厚的尾部。鉴于标准Lasso估计量在此类情形下表现欠佳，我们通过GLS Lasso估计目标参数，并在更一般化条件下拓展了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精确，而当$T,p\to \infty$时，一般条件下Lasso的估计速率趋于平缓。此外，我们采用去偏Lasso对目标参数进行统一推断。蒙特卡洛模拟结果验证了所提估计量的有效性，其在效率上显著优于传统方法。