LASSO-driven inference in time and space
Victor Chernozhukov, Wolfgang Karl Härdle, Chen Huang, Weining Wang
The Annals of Statistics · 2021 · Volume 49 · Issue 3
Abstract
We consider the estimation and inference in a system of high-dimensional regression equations allowing for temporal and cross-sectional dependency in covariates and error processes, covering rather general forms of weak temporal dependence. A sequence of regressions with many regressors using LASSO (Least Absolute Shrinkage and Selection Operator) is applied for variable selection purpose, and an overall penalty level is carefully chosen by a block multiplier bootstrap procedure to account for multiplicity of the equations and dependencies in the data. Correspondingly, oracle properties with a jointly selected tuning parameter are derived. We further provide high-quality de-biased simultaneous inference on the many target parameters of the system. We provide bootstrap consistency results of the test procedure, which are based on a general Bahadur representation for the Z-estimators with dependent data. Simulations demonstrate good performance of the proposed inference procedure. Finally, we apply the method to quantify spillover effects of textual sentiment indices in a financial market and to test the connectedness among sectors.
Keywords
62F40, 62J99, 62M10, Bahadur representation, Lasso, martingale decomposition, simultaneous inference, system of equations, time series, Z-estimation
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