Research Of Stock Network "adaptive" De-noising Method Based On Random Matrix Theory

Stock market is a highly complex dynamic system,so the correction study among stocks is of great value to master the internal structure and evolution rules.Random matrix theory(RMT)is extensively applied into nuclear physics,chaotic system and the wireless communication.Lots of noise signals in the matrix could be found out by introducing the RMT to stock market.Meanwhile,researchers point out that RMT could be used to filter stock market,of which the methods including LCPB(Laloux L,Cizeau P,Potters M,Bouchaud J P),PG+(Plerou V,Gopikrishnan P),KR(Sharifi S,Grane M,Shamaie A)and WLY(Wu Ling Yan).However,the stock market features,as an organic life,vary in different stages is ignored when it comes to the de-noising merits evaluation.So the most effective de-noising method in each stock market stage has not been studied sufficiently.Based on this,this paper try to classify the stock market with the consider of the rules of the development of stock itself.Based on the effects of the four kinds of RMT de-noising method,the adaptive de-noising method is established.The main work and creative points as follows:(1)This paper select the data of eight stock markets,which are the Dow Jones China 88,Shanghai Stock Exchange 884,Hong Kong's Hang Seng 50,South Korea KOSPI200,Taiwan's Weighted Price 200,Australia 200,Nikkei 225 and S&P 500,the normality distribution degree and the descriptive statistics of the market data is explored,and the reasonable criteria for classification based on partial values is established.The stock market is divided into three categories: emerging,development and maturity.(2)These three types of different stock markets are filtered by four different RMT methods respectively.Firstly,compare the motif and robustness in stock-net with the effectiveness of the four methods.Under the discussion of the outcomes of market portfolio in four methods,the adaptive de-noising method for stock-net is constructed,namely: WLY for emerging stage,PG+ for development stage and KR for maturity stage.Finally,the effectiveness of the adaptive de-noising methods is verified in South-Africa 40 Index.(3)To solve the combination investment problem,the Monte Carlo simulation-modification RMT method is presented.Conduct the testing analysis with the data of Dow Jones China 88 and Hong Kong's Hang Seng 50.The validity and practicability of the simulation-modification is verified on eigenvalues,eigenvectors,inverse participation ratio and portfolio.