ℓ 2-Relaxation: With Applications to Forecast Combination and Portfolio Analysis

• 成果类型: Article
• 署名作者: Shi, Zhentao; Su, Liangjun; Xie, Tian
• 署名单位: University System of Georgia; Georgia Institute of Technology; Chinese University of Hong Kong; Tsinghua University; Shanghai University of Finance & Economics
• 刊物名称: REVIEW OF ECONOMICS AND STATISTICS
• ISSN/ISSBN: 0034-6535
• DOI: 10.1162/rest_a_01261
• 发表日期: 2025-03
• 页码: 523-538
• 关键词: covariance-matrix; Nonlinear Shrinkage; variable selection; grouped patterns; CLASSIFICATION

摘要

We propose & ell;( 2)-relaxation, which is a novel convex optimization problem, to tackle a forecast combination with many forecasts or a minimum variance portfolio with many assets. & ell;( 2)-relaxation minimizes the squared Euclidean norm of the weight vector subject to a set of relaxed linear inequalities to balance the bias and variance. It delivers optimality with approximately equal within-group weights when latent block equicorrelation patterns dominate the high-dimensional sample variance-covariance matrix of the individual forecast errors or the assets. Its wide applicability is highlighted in three real data examples in microeconomics, macroeconomics, and finance.