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Title: Lasso-driven inference in time and space Authors:  Chen Huang - University of St. Gallen (Switzerland) [presenting]
Victor Chernozhukov - MIT (United States)
Wolfgang Haerdle - HU Berlin (Germany)
Weining Wang - City U of London (United Kingdom)
Abstract: The estimation and inference in a system of high-dimensional regression equations is considered 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.