【作者】 王莹莹；

【导师】 詹文杰；

【作者基本信息】 华中科技大学 ， 管理科学与工程， 2006， 硕士

【摘要】 有效市场假说是建立在理性投资者、有效市场及随机游走过程这三个核心前提假定基础上的。有效市场假说成立依赖于市场呈独立正态分布、方差存在的假设,但是现实市场是一个复杂的相互依存的系统。许多情况是有效市场假说无法解释得,例如规模效应、季节效应等。因此,众多的研究人员开始关注一些非线性理论在金融市场的运用,典型的有突变理论、协同市场假定、行为金融理论、分形市场假说等。分形理论是非线性分析方法中的一种,由于它能有效的解释自然和经济现象中许多及其复杂多变的问题,因此它已经成为非线性资本市场理论的有力分析工具。本文共分为五个部分,第一部分:简要介绍了有效市场假说理论(EMH)及分形市场假说理论(FMH)的发展及主要思想;并列举了国内外的研究现状。第二部分:详细介绍了分形理论的主要参数Hurst指数及多重分形谱的计算方法。第三部分:利用上证指数1991年1月2日至2005年8月31日及深圳成指1991年4月1日至2006年1月8日的日收盘价为样本数据进行分析,并由此得出中国股票市场的分形特性。第四部分:任选上证指数、深圳成指的一段数据进行多重分形分析,并利用盒维数法对上证指数进行多重谱函数分析,得出沪深股市皆具有多重分形特征。第五部分:结论及展望。通过对上证指数日收盘价的研究发现,沪市存在明显的多重分形特征,但仅用传统的打乱顺序计算Hurst指数无法证明其分形性,必须与V统计量结合使用;通过实证研究得到了上证指数存在一个300天的非循环周期,H值为0.626358,深圳成指存在一个为期1200天的非循环周期,H值为0.590986;利用盒维数法计算多重分形谱函数证明了股票市场的多重分形性。更多还原

【Abstract】 EMH is necessary to prove that price follows a random walk model. But EMH is established on market, which is independent normal distribution and variance existing. But the market is a complicated interdependent system. A lot of cases are what EMH can’t explain, such as scale effect, season effect etc. So a lot of theories that explain these special cases have appeared, such as catastrophe theory, behavior finance theory, coherent market theory and the fractal market theory, which let researchers taking more attention more about the use of non-linear theory in financial market.Fractal theory is one kind of nonlinear analysis and has only decades since it developed, because it can efficiently expenses many complicated problem, such as economics phenomena, so it has became the strong analysis tool of the nonlinear capital market theory.There are five parts in our paper, the first is introduced simply the theories of EMH and FMH; the second is introduced particularly the method of Hurst index and multifractal; and in the third we get the conclusion that China stock market is FMH with analysis using the date of Shanghai from 2 Jan. 1991 to 31 Aug. 2005 and Shenzhen from 1 Apr. 1991 to 8 Jan. 2006; in the forth we get the conclusion that China stock market is MFMH with analysis the date of Shanghai and Shenzhen. The fifth is conclusion and expectation.In our paper, researching on the index of shanghai and Shenzhen bond market, we find that our bond market has obvious fractal character, and working out the Hurst index and V index, which prove that our bond market can be test by non-linear theory. We can get the 300 days as a period, and the H is 0.626358 of shanghai bond market; the same as 1200 days and H is 0.590986 of Shenzhen bond market. In the last we use Box-counting method to prove that Shanghai and Shenzhen bond market is mutifractal.更多还原