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.
Funding Statement
Financial support from the Deutsche Forschungsgemeinschaft via IRTG 1792 “High Dimensional Non Stationary Time Series”, Humboldt-Universität zu Berlin, is gratefully acknowledged.
Acknowledgments
We thank Oliver Linton, Bryan Graham, Manfred Deistler, Hashem Pesaran, Michael Wolf, Valentina Corradi, Zudi Lu, Liangjun Su, Peter Phillips, Frank Windmeijer, Wenyang Zhang and Likai Chen for helpful comments and suggestions. We also thank the Editor and the two anonymous referees for their valuable comments. We remain responsible for any errors or omissions.
Chen Huang is the corresponding author.
Citation
Victor Chernozhukov. Wolfgang Karl Härdle. Chen Huang. Weining Wang. "LASSO-driven inference in time and space." Ann. Statist. 49 (3) 1702 - 1735, June 2021. https://doi.org/10.1214/20-AOS2019
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