LASSO-Driven Inference in Time and Space
76 Pages Posted: 15 Jun 2018 Last revised: 15 May 2020
Date Written: April 25, 2019
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 dependence. A sequence of large-scale regressions with LASSO is applied to reduce the dimensionality, 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: LASSO, Time Series, Simultaneous Inference, System of Equations, Z-estimation, Bahadur Representation, Martingale Decomposition
JEL Classification: C12, C22, C51, C53
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