Penalized Optimal Forecast Combination for Quantile Regressions

Haowen Bao, Zongwu Cai, Yuying Sun and Shouyang Wang
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Haowen Bao: State Key Laboratory of Mathematical Sciences, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China and School of Economics and Management, and MOE Social Science Laboratory of Digital Economic Forecasts and Policy Simulation, University of Chinese Academy of Sciences, Beijing, China
Zongwu Cai: Department of Economics, The University of Kansas, Lawrence, KS 66045, USA
Yuying Sun: State Key Laboratory of Mathematical Sciences, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China and School of Economics and Management, and MOE Social Science Laboratory of Digital Economic Forecasts and Policy Simulation, University of Chinese Academy of Sciences, Beijing, China
Shouyang Wang: State Key Laboratory of Mathematical Sciences, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, China and School of Economics and Management, and MOE Social Science Laboratory of Digital Economic Forecasts and Policy Simulation, University of Chinese Academy of Sciences, Beijing, China

No 202514, WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS from University of Kansas, Department of Economics

Abstract: This paper develops a novel forecast combination approach for quantile regressions (QR) that accommodate both linear and nonlinear forms for parameters and regressors. We propose a penalized weight choice criterion based on the Kullback-Leibler loss in a quasi-likelihood framework that allows parameter uncertainty and model misspecification. This criterion simultaneously selects optimal combination weights and reduces model complexity, which covers special cases such as the Mallows-type criterion in linear QR. First, we prove the asymptotic optimality of the proposed combination method in diverging-dimensional settings for both linear and nonlinear QR cases. Second, we establish the consistency of the selected weights either for the misspecified and correctly specified candidate models, which complements existing model averaging literature for QR that only focuses on asymptotic optimality. Finally, we examine finite sample performance through Monte Carlo simulations and demonstrate advantages over existing methods via an empirical application to excess return forecasting.

Keywords: Asymptotic optimality; Forecast combination; Misspecification; Quantile regressions; Weight convergence (search for similar items in EconPapers)
JEL-codes: C51 C52 C53 (search for similar items in EconPapers)
Date: 2023-01, Revised 2025-05
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