  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.
