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Volume 1,Issue 7

Fall 2025

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20 September 2025

基于高维协方差矩阵估计的投资组合优化策略比较与分析

章爽 孙1 婷 张2 宇雷 万3 国强 王1
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1 上海工程技术大学 数理与统计学院, 中国
2 菏泽职业学院 信息工程系, 中国
3 上海金仕达软件科技股份有限公司 金仕达研究院, 中国
ASDS 2025 , 1(7), 91–96; https://doi.org/10.61369/ASDS.2025070019
© 2025 by the authors. Licensee Art and Design, USA. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution -Noncommercial 4.0 International License (CC BY-NC 4.0) ( https://creativecommons.org/licenses/by-nc/4.0/ )
Abstract

在金融领域,协方差矩阵的精确估计对于优化投资组合至关重要。研究旨在综合比较无条件协方差矩阵估计和条件协方差矩阵估计在投资组合优化中的表现,并基于不同维度的股票和商品两种大类资产的数据进行投资组合优化的实证分析。结果显示:对于低维情形,无条件协方差矩阵估计在组合收益和组合风险偏差方面均具有突出表现;对于高维情形,条件协方差矩阵估计的表现更为有效。

Keywords
协方差矩阵估计
条件协方差
压缩估计
稀疏估计
投资组合优化
References

[1]ENGEL J,BUYDENS L,BLANCHET L. An overview of large-dimensional covariance and precision matrix estimators with applications in chemometrics[J]. Journal of Chemometrics,2017,31(4): e2880.
[2]SUN R,MA T,LIU S,et al. Improved covariance matrix estimation for portfolio risk measurement: a review[J]. Journal of Risk and Financial Management,2019,12(1): 48.
[3]LI D. Estimation of large dynamic covariance matrices: A selective review[J]. Econometrics and Statistics,2024,29: 16-30.
[4]LEDOIT O,WOLF M.A well-conditioned estimator for large-dimensional covariance matrices[J]. Journal of Multivariate Analysis,2004,88(2): 365-411.
[5]LEDOIT O,WOLF M. Nonlinear shrinkage estimation of large-dimensional covariance matrices[J]. The Annals of Statistics,2012,40(2): 1024-1060.
[6]ZHANG Y,TAO J Y,YIN Z X,et al. Improved large covariance matrix estimation based on efficient convex combination and its application in portfolio optimization[J]. Mathematics,2022,10(22): 4282.
[7]LEDOIT O,WOLF M. The power of (non-)linear shrinking: A review and guide to covariance matrix estimation[J]. Journal of Financial Econometrics,2020,20(1): 187-218.
[8]FAN J Q,FAN Y Y,LV J C. High dimensional covariance matrix estimation using a factor model[J]. Journal of Econometrics,2008,147(1): 186-197.
[9]FAN J Q,LIAO Y,MARTINA M. Large covariance estimation by thresholding principal orthogonal complements[J]. Journal of the Royal Statistical Society Series B: Statistical Methodology,2013,75(4): 603-680.
[10] 杨小卜. 基于因子收缩方法的高维协方差估计[J]. 数学的实践与认识,2022,52(10): 94-103.
[11]RUAN Y W,ZHANG X F,LIU Y J. A semi-parametric factor-GARCH model for high dimensional covariance matrix estimation[J]. Journal of the Korean Statistical Society,2025: 1-32.
[12]FAN J Q,LIAO Y,LIU H. An overview of the estimation of large covariance and precision matrices[J]. The Econometrics Journal,2016,19(1): 1-32.
[13]ROTHMAN A J,LEVINA E,ZHU J.Generalized thresholding of large covariance matrices[J]. Journal of the American Statistical Association,2009,104(485): 177-186.
[14]XIAO Y H,LI P L,LU S. Sparse estimation of high-dimensional inverse covariance matrices with explicit eigenvalue constraints[J]. Journal of the Operations Research Society of China,2021,9: 543-568.
[15] 宋鹏,胡永宏. 基于已实现协方差矩阵的高维金融资产投资组合应用[J]. 统计与信息论坛,2017,32(08): 63-70.
[16] 王鑫,孔令臣,王力群. 高维协方差矩阵的估计问题[J/OL]. 运筹学学报,1-14[2025-05-30]. http://kns.cnki.net/kcms/detail/31.1732.O1.20240202.1134.006.html.
[17]ENGLE R. Dynamic conditional correlation: A simple class of multivariate generalized autoregressive conditional heteroskedasticity models[J]. Journal of Business and Economic Statistics,2002,20(3): 339-350.
[18]FISZEDER P,FALDZINSKI M,MOLNAR P. Modeling and forecasting dynamic conditional correlations with opening,high,low,and closing prices[J]. Journal of Empirical Finance,2023,70: 308-321.
[19]JARJOUR R,CHAN KS.Dynamic conditional angular correlation[J]. Journal of Econometrics,2020,216(1): 137-150.
[20]SUN Z S,GAO X Y,LUO K Y,et al. Enhancing high-dimensional dynamic conditional angular correlation model based on garch family models: Comparative performance analysis for portfolio optimization[J]. Finance Research Letters,2025,75: 106808.
[21] 刘丽萍,马丹,白万平. 大维数据的动态条件协方差阵的估计及其应用[J]. 统计研究,2015,32(6): 105-112.
[22] 刘进. 条件协方差矩阵的估计方法研究综述[J]. 统计与决策,2019,35(23): 23-27.
[23]LEDOIT O,WOLF M. Shrinkage estimation of large covariance matrices: Keep it simple,statistician?[J]. Journal of Multivariate Analysis,2021,186: 104796.
[24]FRIEDMAN J,HASTIE T,TIBSHIRANI R. Sparse inverse covariance estimation with the graphical lasso[J]. Biostatistics,2008,9(3): 432-441.
[25]ALEXANDER K,MEMMEL C. Estimating the global minimum variance portfolio[J]. Schmalenbach Business Review,2006,58: 332-348.
[26]DE NARD G,ENGLE R F,LEDOIT O,et al. Large dynamic covariance matrices: Enhancements based on intraday data[J]. Journal of Banking and Finance,2022,138: 106426.

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