Inference for high-dimensional regressions with heteroskedasticity and autocorrelation

摘要: Time series regression analysis relies on the heteroskedasticity- and autocorrelation-consistent (HAC) estimation of asymptotic variance to conduct proper inference. This paper develops such inferential methods for high-dimensional time regressions. To recognize data structures we focus sparse-group LASSO estimator. We establish debiased central limit theorem low dimensional groups coefficients study HAC estimator long-run based residuals. The treatment a new Fuk-Nagaev inequality class $\tau$-dependent processes with heavier than Gaussian tails, which is independent interest.