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LASSO-Driven Inference in Time and Space

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  • V. Chernozhukov, Massachusetts Institute of Technology
  • ,
  • W.K. Härdle, Humboldt-Universität zu Berlin, Berlin
  • ,
  • Chen Huang
  • W. Wang, University of York

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.

OriginalsprogEngelsk
TidsskriftAnnals of Statistics
Vol/bind49
Nummer3
Sider (fra-til)1702-1735
Antal sider34
ISSN0090-5364
DOI
StatusUdgivet - jun. 2021

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