Research On The Aplication Of Random Matrix In A Share Market

The volatility of stock price is of centricity and randomness,which can be explored from the theoretical and practical levels.In order to make correct investment decisions,the investors analyze the company's financial statements,the K-line chart and the industry research report.The impact of national policies on related industries and the impact of political,economic and military situations on A share market at home and abroad are all important factors affecting the stock market.But the stock market isunpredictable,and it is often difficult to analyze and explain it by linear methods.Therefore,it is of great significance to make an in-depth analysis of the related structure between the stocks.Generally speaking,the stock market can be regarded as a complex system of nonlinear interaction between stocks,and the relationship between stocks is changing.At this time,the state of the complex system is also changing.The random matrix theory can be used to calculate the average results of all the interactions contained in the complex system.The statistical difference between the empirical correlation matrix of return and the random correlation matrix reflects the nonrandom properties of the real system.In this thesis,thestock market is non random through the random matrix analysis of some shares of CSI 300 index and CBI 500 index.Except for the largest eigenvalue representing the market influence,there are several eigenvalues above the upper bounds of the eigenvalues predicted by the random matrix theory.The corresponding eigenvector elements can be divided into several positive and negative subsectors.The subsector structures are studied and the anti-correlation between the positive and negative subsectors is analyzed.Through the comparison of the two empirical results,it is found that the subsector structures of the CSI 300 index has more obvious industry characteristics,while the CBI 500 index is not.The dissipative structure theory of the open complex system and the evolvement of the network entropy which describes the robustness of the complex network can explain the empirical results of the stochastic matrix theory from the angle of the evolution of the system.By using the empirical results of random matrix,the relationship between industries is obtained,so that investors can judge the situation of other industries in the case of some industry indicators.Because the correlation between stocks in positive and negative subsectors is relatively low,the empirical results of random matrices can be used to construct stock portfolios.The results of this thesis can provide a reference for investment decision.