基于蒙特卡罗模拟修正的随机矩阵去噪方法

Random matrix denoising method based on Monte Carlo simulation as amended

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。

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.