Random matrix denoising method based on Monte Carlo simulation as amended

doi:10.11772/j.issn.1001-9081.2016.09.2642

Journal of Computer Applications ›› 2016, Vol. 36 ›› Issue (9): 2642-2646.DOI: 10.11772/j.issn.1001-9081.2016.09.2642

Random matrix denoising method based on Monte Carlo simulation as amended

LUO Qi¹, HAN Hua¹, GONG Jiangtao¹, WANG Haijun²

1. School of Science, Wuhan University of Technology, Wuhan Hubei 430070, China;
2. School of Management, Huazhong University of Science and Technology, Wuhan Hubei 430074, China

Received:2016-01-15 Revised:2016-03-08 Online:2016-09-08 Published:2016-09-10
Supported by:
This work is partially supported by the Fundamental Research Funds for the Central Universities (2015-zy-115), the National Natural Science Foundation of China (71372135).

基于蒙特卡罗模拟修正的随机矩阵去噪方法

骆旗¹, 韩华¹, 龚江涛¹, 王海军²

1. 武汉理工大学理学院, 武汉 430070;
2. 华中科技大学管理学院, 武汉 430074

通讯作者: 韩华
作者简介:骆旗(1990-),女,河南南阳人,硕士研究生,主要研究方向:股票网络、随机矩阵理论去噪;韩华(1975-),女,山东烟台人,教授,博士,主要研究方向:复杂网络、经济控制与决策;龚江涛(1990-),男,安徽安庆人,硕士研究生,主要研究方向:节点重要性评价;王海军(1970-),男,江苏如东人,教授,博士,主要研究方向:管理科学与工程、运营管理。
基金资助:
中央高校基本科研业务费专项资金资助项目（2015-zy-115）；国家自然科学基金面上项目（71372135）。

Abstract

Abstract: Since the small combined stock market has less noise information, a random matrix denoising method amended by Monte Carlo simulation was proposed. Firstly, random matrix was generated by simulation; secondly, the lower and upper bounds of the noise were corrected simultaneously by using a large number of simulated data; finally, the range of noise was determined precisely. The Dow Jones China 88 Index and the Hang Seng 50 Index were used for empirical analysis. The simulation results show that, compared with LCPB (Laloux-Cizeau-Potters-Bouchaud), PG+(Plerou-Gopikrishnan) and KR (RMT denoising method based on correlation matrix eigenvector's Krzanowski stability), rationality and validity of the noise range corrected by Monte Carlo simulation denoising method are greatly improved in eigenvalue, eigenvector and inverse participation ratio. Investment portfolio of the correlation matrix before and after denoising was given, and the results indicate that the Monte Carlo simulation denoising method has the smallest value at risk under the same expected rate of return, which can provide a certain reference for the portfolio selection, risk management and other financial applications.

Key words: Monte Carlo simulation, random matrix theory, denoising method, small combination, portfolio

摘要： 针对蕴含噪声信息较少的小组合股票市场，提出使用蒙特卡罗模拟修正的随机矩阵去噪方法。首先通过数据模拟生成随机矩阵，然后利用大量的模拟数据来同时修正噪声下界和上界，最终对噪声范围进行精确测定。运用道琼斯中国88指数和香港恒生50指数的数据进行实证分析，结果表明，与LCPB法、PG+法和KR法相比，在特征值、特征向量和反比参率方面，蒙特卡罗模拟去噪方法修正后噪声范围的合理性及有效性得到很大的提升；对去噪前后的相关矩阵进行投资组合，得知在相同的期望收益率下，蒙特卡罗模拟去噪方法具有最小的风险值，能够为资产组合选择和风险管理等金融应用提供一定的参考。

关键词: 蒙特卡罗模拟, 随机矩阵理论, 去噪方法, 小组合, 投资组合

CLC Number:

N949

LUO Qi, HAN Hua, GONG Jiangtao, WANG Haijun. Random matrix denoising method based on Monte Carlo simulation as amended[J]. Journal of Computer Applications, 2016, 36(9): 2642-2646.

骆旗, 韩华, 龚江涛, 王海军. 基于蒙特卡罗模拟修正的随机矩阵去噪方法[J]. 计算机应用, 2016, 36(9): 2642-2646.

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Random matrix denoising method based on Monte Carlo simulation as amended

基于蒙特卡罗模拟修正的随机矩阵去噪方法

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