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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.
Original language | English |
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Journal | Annals of Statistics |
Volume | 49 |
Issue | 3 |
Pages (from-to) | 1702-1735 |
Number of pages | 34 |
ISSN | 0090-5364 |
DOIs | |
Publication status | Published - Jun 2021 |
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ID: 200036004