Before revision:  We derive a new Fuk-Nagaev inequality for a class of \tau-dependent processes with heavier than Gaussian tails, nesting \alpha-mixing processes as a special case, and establish estimation, prediction, and inferential properties, including convergence rates of the HAC estimator for the long-run variance based on LASSO residuals.
After revision:  We establish the debiased central limit theorem for low dimensional groups of regression coefficients and study the HAC estimator of the long-run variance based on the sparse-group LASSO residuals. The treatment relies on a new Fuk-Nagaev inequality for a class of \tau-dependent processes with heavier than Gaussian tails, nesting \alpha-mixing processes as a special case, and establish estimation, prediction, and inferential properties, including convergence rates of the HAC estimator for the long-run variance based on LASSO residuals.