Research On The Non-linearity And Noise In The Stock Market

With the deep research into the financial markets,people have gradually found out the serious defect of classic linear theory.Various test results and evidence have also proved that the stock market under the influence of multiple factors is a nonlinear dynamic system.Meanwhile,the limitation of methods and computation tools combining with the influence of random factors bring noise into the time series data of stock pnce.Based on the premise,the thesis analyses the noise data that have really existed and uses the nonlinear theory of Chaos and Fractal to assay and predict the idea time series data of stock price without noise. But how to effectively discover noise from the chaos data and determine the degree of the influence of noise,thus to improve the short term forecast ability of stock market is still a question which need us to research thoroughly.There are five chapters in this thesis.The first chapter-the basic Chaos and Fractal theory.After summarizing the invalidation of linear theory in financial markets,the author detailedly introduces the nonlinear dynamic system, basic Chaos and Fractal theory,and show the relation between Chaos and Fractal theory.The second chapter-the noise in time series data of stock pnce.Based on the analysis of diverse factors that influence the fluctuation of stock price ,the author sets forth that existence of random factors will result in the appearance of noise.Then theoretically bounds the chaos data with noise and gives several effective methods to differentiate them.Finally the author provides some noise analytic means.The third chapter-the study on the chaos and fractal feature of China stock market.Under the hypothesis of empty of noise,utilizing technology of phase-space reconstruction to empirically study the chaos and fractal feature of China stock market.Separately computing the Lyapunov exponents and fractal dimension,and using nerve network to achieve short term forecast of the stock price.The fourth chapter-the transaction of noise.Expounding the difficulties andquestions that the noise has brought into the research of Chaos and Fractal. Furthermore, according to the irregular and complex feature of the disorder random system and the problem of exactly quantifying the influence factors,there are fairly great difficulties in getting rid of noise.Through analyzing the present conditions of noise transaction technology ,the author points out that eliminating noise from the Chaos system still need our further research.The last chapter-conclusion of the whole thesis.The innovation work of the thesis:(1)analyzing the real existence of noise in time series data of stock price,and on the basis of theoretically bounding the chaos data with noise,giving methods to separate noise from chaos data;(2)detailedly expounding data mining and rough set used in noise analysis,and independently finishing the noise analysis by using clustering,association analysis and rough set;(3)discussing the choice of embedding dimension and delay time in phase-space reconstruction technology;(4) utilizing nerve network algorithm to short term predict the stock price,proposing the view that by continuously using training specimen to change the weigh,thus to improve the accuracy of forecast;(5)elaborating on the present conditions and difficulties of noise transaction.