@article{e91f06ca7846409d8c19c91446a11df3,
title = "On LASSO for Predictive Regression",
abstract = "Explanatory variables in a predictive regression typically exhibit low signal strength and various degrees of persistence. Variable selection in such a context is of great importance. In this paper, we explore the pitfalls and possibilities of the LASSO methods in this predictive regression framework. In the presence of stationary, local unit root, and cointegrated predictors, we show that the adaptive LASSO cannot asymptotically eliminate all cointegrating variables with zero regression coefficients. This new finding motivates a novel post-selection adaptive LASSO, which we call the twin adaptive LASSO (TAlasso), to restore variable selection consistency. Accommodating the system of heterogeneous regressors, TAlasso achieves the well-known oracle property. In contrast, conventional LASSO fails to attain coefficient estimation consistency and variable screening in all components simultaneously. We apply these LASSO methods to evaluate the short- and long-horizon predictability of S&P 500 excess returns.",
keywords = "Cointegration, Machine learning, Nonstationary time series, Shrinkage estimation, Variable selection",
author = "Lee, {Ji Hyung} and Zhentao Shi and Zhan Gao",
note = "Funding Information: We would like to thank the Editor, Serena Ng, the Associate Editor, and two anonymous referees for their thoughtful comments, which substantially improved this paper. We thank Mehmet Caner, Zongwu Cai, Yoosoon Chang, Changjin Kim, Bonsoo Koo, Zhipeng Liao, Tassos Magdalinos, Joon Park, Hashem Pesaran, Peter Phillips, Kevin Song, Jing Tao, Keli Xu, Jun Yu, and the seminar participants at Kansas, Indiana, Purdue, UBC, UW, Duke, KAEA, IPDC, AMES, and IAAE conferences for helpful comments. We also thank Bonsoo Koo for sharing the data for the empirical application. Shi acknowledges the financial support of the the Research Grants Council of Hong Kong No. 24614817 and No. 14500118. All remaining errors are ours. Funding Information: We would like to thank the Editor, Serena Ng, the Associate Editor, and two anonymous referees for their thoughtful comments, which substantially improved this paper. We thank Mehmet Caner, Zongwu Cai, Yoosoon Chang, Changjin Kim, Bonsoo Koo, Zhipeng Liao, Tassos Magdalinos, Joon Park, Hashem Pesaran, Peter Phillips, Kevin Song, Jing Tao, Keli Xu, Jun Yu, and the seminar participants at Kansas, Indiana, Purdue, UBC, UW, Duke, KAEA, IPDC, AMES, and IAAE conferences for helpful comments. We also thank Bonsoo Koo for sharing the data for the empirical application. Shi acknowledges the financial support of the the Research Grants Council of Hong Kong No. 24614817 and No. 14500118 . All remaining errors are ours. Publisher Copyright: {\textcopyright} 2021 Elsevier B.V.",
year = "2021",
month = mar,
day = "10",
doi = "10.1016/j.jeconom.2021.02.002",
language = "English (US)",
journal = "Journal of Econometrics",
issn = "0304-4076",
publisher = "Elsevier BV",
}