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LASSO-Driven Inference in Time and Space

Chernozhukov, V., Härdle, W.K., Huang, C. and Wang, W. (2018). LASSO-Driven Inference in Time and Space (18/04). London, UK: Department of Economics, City, University of London.

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.

Publication Type: Monograph (Discussion Paper)
Publisher Keywords: LASSO, time series, simultaneous inference, system of equations, Z-estimation, Bahadur representation, martingale decomposition
Subjects: H Social Sciences > HB Economic Theory
Departments: School of Arts & Social Sciences > Economics > Discussion Paper Series
URI: http://openaccess.city.ac.uk/id/eprint/20231
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