Penalized Model Averaging for High Dimensional Quantile Regressions

Haowen Bao, Zongwu Cai, Yuying Sun and Shouyang Wang
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Haowen Bao: School of Economics and Management, University of Chinese Academy of Sciences and Academy of Mathematics and Systems Science, Chinese Academy of Sciences, China
Zongwu Cai: Department of Economics, The University of Kansas, Lawrence, KS 66045, USA
Yuying Sun: School of Economics and Management, University of Chinese Academy of Sciences and Academy of Mathematics and Systems Science, Chinese Academy of Sciences, China
Shouyang Wang: School of Economics and Management, University of Chinese Academy of Sciences, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, China, and School of Entrepreneurship and Management, ShanghaiTech University, China

No 202302, WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS from University of Kansas, Department of Economics

Abstract: This paper proposes a new penalized model averaging method for high dimensional quantile regressions based on quasi-maximum likelihood estimation, which determines optimal combination weights and yields sparseness from various potential covariates simultaneously. The proposed weight choice criterion is based on the Kullback-Leibler loss with penalties, which could reduce to Mallows-type criterion for asymmetric Laplace density, and both the dimension of covariates and the number of possibly misspecified candidate models are allowed to be diverging with the sample size. Also, the asymptotic optimality and convergence rate of the selected weights are derived under time series framework, even when all candidate models are misspecified. We further extend our concern to the ultra-high dimensional scenarios and establish the corresponding asymptotic optimality. Simulation studies and empirical application to stock returns forecasting illustrate that the proposed method outperforms existing methods.

Keywords: High-dimensional quantile regressions; Optimality; Consistency; Kullback-Leibler loss; Model averaging (search for similar items in EconPapers)
JEL-codes: C32 C52 (search for similar items in EconPapers)
Date: 2023-01
New Economics Papers: this item is included in nep-ecm and nep-ets
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