Square‐Root Lasso for High‐Dimensional Sparse Linear Systems with Weakly Dependent Errors

27 Pages Posted: 14 Feb 2018

See all articles by Fang Xie

Fang Xie

University of Macau - Department of Mathematics

Zhijie Xiao

Boston College - Department of Finance and Department of Economics

Date Written: March 2018

Abstract

We study the square‐root LASSO method for high‐dimensional sparse linear models with weakly dependent errors. The asymptotic and non‐asymptotic bounds for the estimation errors are derived. Our results cover a wide range of weakly dependent errors, including ‐mixing, ‐mixing, ‐mixing, and ‐dependent types. Numerical simulations are conducted to show the consistency property of square‐root LASSO. An empirical application to financial data highlights the importance of the results and method.

Keywords: high‐dimensional linear model, square‐root LASSO, ‐mixing, ‐mixing, ‐mixing, ‐dependent, estimation consistency

Suggested Citation

Xie, Fang and Xiao, Zhijie, Square‐Root Lasso for High‐Dimensional Sparse Linear Systems with Weakly Dependent Errors (March 2018). Journal of Time Series Analysis, Vol. 39, Issue 2, pp. 212-238, 2018, Available at SSRN: https://ssrn.com/abstract=3122744 or http://dx.doi.org/10.1111/jtsa.12278

Fang Xie (Contact Author)

University of Macau - Department of Mathematics

P.O. Box 3001
Macau

Zhijie Xiao

Boston College - Department of Finance and Department of Economics ( email )

United States

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