【作者】 吴艳；

【导师】 周万隆；

【作者基本信息】 武汉大学 ， 技术经济及管理， 2004， 硕士

【摘要】 随着对金融市场研究的深入，人们逐渐发现传统线性理论有着严重的缺陷，各种各样的检验结果和证据都表明，众多因素影响下的股票市场是一个非线性的动力学系统。与此同时，方法和计算工具的限制以及随机因素的影响使得股票价格的时间序列不可避免的带有噪音。本文在此前提下，对客观存在的噪音数据进行了分析，并对理想化的、无噪音的股价时序数据运用混沌、分形理论进行分析、预测。但如何有效地从实测数据中发现噪音，并判定噪音的影响程度，以此来提高股票市场的短期预测能力，仍是一个值得我们深究的问题。 全文共分为五章。 第一章——混沌与分形的基本理论。在概述了金融市场线性理论失灵的背景下，详细介绍了非线性动力学系统、混沌与分形的基本理论，给出了混沌与分形理论间的联系。 第二章——股票价格时间序列中的噪音。在分析了影响股票价格变动的各种因素的基础上，提出了随机的因素将导致股价时序中噪音数据的出现。从理论上界定了混沌数据与噪音，并给出了有效区分混沌数据与噪音的方法。最后给出了几种噪音分析方法。 第三章——中国股票市场的混沌、分形研究。在股价时序数据不存在噪音的假设前提下，利用相空间重构技术对中国股票市场的混沌与分形特征进行实证研究。分别计算出Lyapunov指数和分维数，并利用神经网络方法对股票价格进行短期预测。 第四章——噪音的处理。提出噪音给混沌、分形研究所带来的困难和引发的问题，且针对无序随机系统的不规则性和复杂性，以及影响因素的准确量化，剔除噪音数据有相当大的难度。通过分析噪音处理技术的现状，说明混沌中噪音的剔除有待深入的研究。 第五章——全文总结。 文中本人的创新工作如下：①分析了股价时序数据中噪音的客观存在性，并在理论上界定了混沌数据与噪音的基础上，给出了区分噪音和混沌数据的方法。②对噪音分析中的数据挖掘方法、粗糙集方法进行了详细的阐述，并独立完成利用数据挖掘中的聚类方法、关联分析和粗糙集理论对噪音的分析。③探讨了相空间重构技术中的嵌入维和时滞的选择问题。④利用神经网络算法对股票价格进行预测，并指出了预测的短期性，提出通过不断使用训练样本改变权值以提高预测准确性的观点。⑤对噪音处理问题的现状和困难进行了阐述和探讨。更多还原

【Abstract】 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.更多还原