Inference for High-Dimensional Regressions With Heteroskedasticity and Auto-correlation
Abstract
Time series regression analysis relies on the heteroskedasticity- and auto-correlation-consistent (HAC) estimation of the asymptotic variance to conduct proper inference. This paper develops such inferential methods for high-dimensional time series regressions. To recognize the time series data structures we focus on the sparse-group LASSO estimator. 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 τ-dependent processes with heavier than Gaussian tails, which is of independent interest.
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https://kenaninstitute.unc.edu/publication/inference-for-high-dimensional-regressions-with-heteroskedasticity-and-auto-correlation/
