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LASSO-Driven Inference in Time and Space

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  • Chernozhukov, Victor
  • Härdle, Wolfgang Karl
  • Huang, Chen
  • Wang, Weining

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 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.

Suggested Citation

  • Chernozhukov, Victor & Härdle, Wolfgang Karl & Huang, Chen & Wang, Weining, 2018. "LASSO-Driven Inference in Time and Space," IRTG 1792 Discussion Papers 2018-021, Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series".
  • Handle: RePEc:zbw:irtgdp:2018021
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    More about this item

    Keywords

    LASSO; time series; simultaneous inference; system of equations; Z-estimation; Bahadur representation; martingale decomposition;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods

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