日内股市数据的小波分形特征研究

发布时间：2018-01-09 19:27

本文关键词：日内股市数据的小波分形特征研究　出处：《首都经济贸易大学》2012年博士论文　论文类型：学位论文

【摘要】：自1970年,法玛提出有效市场假说(Efficient Market Hypothesis, EMH)以来,这一假说就成为了现代金融学的理论基础,并在这个假说的基础上构建起了现代金融学的大厦。但是,20世纪70年代以后,在金融市场上开始出现大量EMH所不能解释的所谓“异象”。因此,自上世纪80年代以来,为了能够更强有力地解释金融市场,众多学者纷纷从不同的方面进行探索,以期发现更符合现实的新理论和新模型。这其中比较有影响的就包括从90年代兴起的分形理论。分形理论认为金融市场的波动是一个非线性动力学系统,具有长程相关性和趋势循环性。分形理论在金融市场的直接应用就产生了分形市场理论。由于该理论并不需要类似有效市场理论那般严格的前提假设,并且它更注重市场的流动性,并且指出投资者的市场行为会因投资期限的改变而相应地发生变化,因此,相应给出的对投资者行为的描述和对市场价格运动模拟的模型也更符合实际。随着这些年来的计算技术和方法的不断进步,对金融数据的研究也开始转向以越来越精细的时刻记录的数据为主了,即高频数据。由于高频数据具有更加详细和精确的反应市场微观结构的特性,因此在揭示市场价格的形成方面、在探索金融风险的测度方面以及在促进资产合理定价,促进衍生品市场形成等方面具有研究价值。 2005年,我国沪深300指数的推出弥补了我国股市一直没有能够反映整体走势的跨市场的统一的指数这一空缺。这一指数的推出为投资者提供了衡量自己证券投资收益情况的基本尺度,并且在此基础上,市场中又推出了以沪深300指数为跟踪目标的指数基金产品,在为中小投资者提供了分散化投资通道的同时也扩大了市场中机构投资者的阵容。因此,对沪深300指数的相关特征的研究就显得尤为必要与迫切。目前,针对沪深300指数的研究还不多。本文就是在分形理论的基础上,运用小波分析的方法,对沪深300指数的日内收益率和收益波动率系列的分形特征进行了较为系统、全面地分析,并且首次在高频收益波动率序列的去噪中引入经验模态分解算法(Empirical Mode Decomposition, EMD)。研究发现,日内高频收益率序列和收益波动率序列不仅具有单分形特征,同时也具有多分形特征,并且在去噪效果方面,经验模态分解算法和小波去噪各具优越。
[Abstract]:Since 1970 , Fama put forward effective market hypothesis ( EMH ) , this hypothesis has become the theoretical foundation of modern finance , and constructed modern financial architecture on the basis of this hypothesis . However , after the 1970s , there appeared a lot of so - called " visions " that EMH could not explain in financial markets . Therefore , since the 1980s , in order to explain the financial markets more forcefully , many scholars have explored different ways to find more realistic new theories and models . The fractal theory holds that the volatility of financial markets is a nonlinear dynamic system , which has long - range correlation and trend - cycle . With the continuous progress of computing technology and method over the years , the research on financial data has also begun to turn to the more and more sophisticated time - recorded data , namely , high - frequency data . As the high - frequency data has the characteristics of more detailed and accurate microstructure of the reaction market , it is valuable to explore the measurement of market price and to promote the reasonable pricing of assets and promote the formation of derivatives market . In 2005 , our stock market has not been able to reflect the unified index of the overall trend across the market . The introduction of the index provides investors with the basic dimension to measure the return of securities investment . On the basis of this , the index fund products with the Shanghai - Shenzhen 300 index as the tracking target are introduced in the market , and the portfolio of institutional investors in the market is expanded . Therefore , the research on the relevant characteristics of the Shanghai - Shenzhen 300 index is especially necessary and urgent . At present , the research on the Shanghai - Shenzhen 300 index is not much . Based on the fractal theory , the fractal characteristics of the daily return and return volatility series of Shanghai - Shenzhen 300 index are systematically and comprehensively analyzed , and Empirical Mode Decomposition ( EMD ) is introduced for the first time in the de - noising of the high - frequency yield fluctuation rate sequence . It is found that the high frequency yield sequence and the yield fluctuation rate sequence have not only the single fractal characteristics but also the multi - fractal characteristics , and the empirical mode decomposition algorithm and wavelet de - noising are superior in terms of denoising effect .

【学位授予单位】：首都经济贸易大学
【学位级别】：博士
【学位授予年份】：2012
【分类号】：F224;F832.51

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