Humboldt-Universität zu Berlin - High Dimensional Nonstationary Time Series

IRTG1792DP2018 021

LASSO-Driven Inference in Time and Space

Victor Chernozhukov
Wolfgang K. Härdle
Chen Huang
Weining Wang

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.

LASSO, time series, simultaneous inference, system of equations, Z-estimation, Bahadur representation, martingale decomposition

JEL classification:
C12, C22, C51, C53