LASSO-Driven Inference in Time and Space

76 Pages Posted: 15 Jun 2018 Last revised: 15 May 2020

See all articles by Victor Chernozhukov

Victor Chernozhukov

Massachusetts Institute of Technology (MIT) - Department of Economics

Wolfgang K. Härdle

Blockchain Research Center; Xiamen University - Wang Yanan Institute for Studies in Economics (WISE); Charles University; National Yang Ming Chiao Tung University; Humboldt University of Berlin - Center for Applied Statistics and Economics (CASE)

Chen Huang

Aarhus University - Department of Economics and Business Economics

Weining Wang

affiliation not provided to SSRN; University of York

Date Written: April 25, 2019

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.

Keywords: LASSO, Time Series, Simultaneous Inference, System of Equations, Z-estimation, Bahadur Representation, Martingale Decomposition

JEL Classification: C12, C22, C51, C53

Suggested Citation

Chernozhukov, Victor and Härdle, Wolfgang K. and Huang, Chen and Wang, Weining and Wang, Weining, LASSO-Driven Inference in Time and Space (April 25, 2019). Available at SSRN: https://ssrn.com/abstract=3188362 or http://dx.doi.org/10.2139/ssrn.3188362

Victor Chernozhukov

Massachusetts Institute of Technology (MIT) - Department of Economics ( email )

50 Memorial Drive
Room E52-262f
Cambridge, MA 02142
United States
617-253-4767 (Phone)
617-253-1330 (Fax)

HOME PAGE: http://www.mit.edu/~vchern/

Wolfgang K. Härdle

Blockchain Research Center ( email )

Unter den Linden 6
Berlin, D-10099
Germany

Xiamen University - Wang Yanan Institute for Studies in Economics (WISE) ( email )

A 307, Economics Building
Xiamen, Fujian 10246
China

Charles University ( email )

Celetná 13
Dept Math Physics
Praha 1, 116 36
Czech Republic

National Yang Ming Chiao Tung University ( email )

No. 1001, Daxue Rd. East Dist.
Hsinchu City 300093
Taiwan

Humboldt University of Berlin - Center for Applied Statistics and Economics (CASE)

Unter den Linden 6
Berlin, D-10099
Germany

Chen Huang (Contact Author)

Aarhus University - Department of Economics and Business Economics ( email )

Fuglesangs Allé 4
Aarhus V, 8210
Denmark

Weining Wang

affiliation not provided to SSRN

University of York ( email )

Department of Economics and Related Studies Univer
York, YO10 5DD
United Kingdom

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