高维时变投资组合模型的构造及估计

刘丽萍, 吕政

系统科学与数学 ›› 2022, Vol. 42 ›› Issue (9) : 2367-2382.

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系统科学与数学 ›› 2022, Vol. 42 ›› Issue (9) : 2367-2382. DOI: 10.12341/jssms21698

高维时变投资组合模型的构造及估计

    刘丽萍1, 吕政2
作者信息 +

Construction and Estimation of High-Dimensional Time-Varying Portfolio Model

    LIU Liping1, Lü Zheng2
Author information +
文章历史 +

摘要

在大数据背景下，高维资产组合的构造以及选择是金融领域研究的热点和难点问题.文章构造了基于SCGARCH模型的含有范数约束的高维时变最小方差投资组合模型，将其记为NC-MVP-SCGARCH.该组合的优势主要体现在两方面：首先采用SCGARCH模型来估计和预测组合的重要输入变量——资产间的协方差阵，该模型将改进的乔列斯基分解法和卡尔曼滤波估计方法相结合，在解决了高维数据所面临的维数诅咒的同时，考虑了过去市场信息对协方差阵估计的影响；其次，基于范数约束的最小方差投资组合（NC-MVP）将l1和l2范数有机结合，更加适用于高维资产.研究发现：文章构造的NC-MVP-SCGARCH组合效果更优.

Abstract

In the context of big data, the construction of high-dimensional asset portfolios as well as their selection is a hot and difficult problem for research in finance. In this paper, we construct a high-dimensional time-varying minimum variance portfolio model with norm constraints based on the SCGARCH model, which is denoted as NC-MVP-SCGARCH. The advantages of the portfolio are twofold:Firstly, SCGARCH model is used to estimate and predict the significant input variables of the portfolio-Covariance matrix between assets, the model combines an improved Cholesky decomposition with a Kalman filter estimation method that addresses the curse of dimensionality faced by high-dimensional data while taking into account the effect of past market information on the estimation of the covariance matrix. Secondly, NC-MVP, a minimum variance portfolio model based on elastic network constraints, will be more applicable to high-dimensional assets by organically combining l1 and l2. It is found that the NC-MVP-SCGARCH constructed in this paper is more effective.

关键词

改进的乔列斯基分解法 / 弹性网络 / 高维时变投资组合 / 状态空间模型 / NC-MVP-SCGARCH模型

Key words

Improved cholesky decomposition / elastic-net / state space model / highdimensional time-varying portfolio / NC-MVP-SCGARCH model

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刘丽萍 , 吕政. 高维时变投资组合模型的构造及估计. 系统科学与数学, 2022, 42(9): 2367-2382. https://doi.org/10.12341/jssms21698
LIU Liping , Lü Zheng. Construction and Estimation of High-Dimensional Time-Varying Portfolio Model. Journal of Systems Science and Mathematical Sciences, 2022, 42(9): 2367-2382 https://doi.org/10.12341/jssms21698
中图分类号： 91G10    91G70   

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基金

贵州省科技厅一般项目（黔科合基础[2019]1050），贵州财经大学校级项目（2020XYB06）资助课题.
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