中国股市分形特征及其应用研究

发布时间：2018-04-11 04:11

本文选题：股票市场 + 分形市场　；参考：《安徽大学》2014年硕士论文

【摘要】：对证券市场价格行为特征的研究一直是学术界和金融投资界中广为关注的热点问题。价格的随机游走性和市场的有效性是主流金融计量理论中重要的理论基石。然而,随着市场的发展,主流的有效市场理论不断受到市场实际运行状况和相关研究的检验。金融物理学研究中的分形理论作为研究金融市场较为合适的工具,能够很大程度的弥补有效市场理论的不足。所以本文运用分形理论,对1996年12月16日至2013年12月31日的上证指数和深证成指的市场特征进行了研究,从市场整体的单分形特征和市场结构的多重分形特征来全面的认识市场。对中国股票市场的单分形特征研究表明：股票市场是一个非线性系统。股价运动并不符合布朗运动和几何布朗运动,相比较而言,分数布朗运动是股价波动一个较好的描述。同时收益率的分布特征,并不能用正态分布很好的描述,而具有尖峰厚尾性的分形分布却可以较好的描述收益率的分布特征。这都表明了以分形市场来理解股票市场更加符合实际情况。整体来看,中国股票市场具有统计自相似性,不同时间标度下的价格走势具有相似的形态,不同时间标度下的收益率具有相似的分布特征。同时,R/S分析表明了中国股票市场是一个非有效的市场,市场具有长记忆性特征,以前价格波动和历史信息会影响以后的股价波动,因此股价在一定程度上是可以预测的。更进一步的对长记忆性的周期测度表明,平均来看,上证指数的长记忆性在30天时会减少、70天时会消失,深证成指的长记忆性在30天时会减少,60天时会消失。单分形特征表明了市场的整体特征,进一步的运用多重分形理论对市场的结构特征进行研究表明：中国股市存在着多重分形结构,股价收益率的大小幅波动之间,以及股价分布的高低价位之间具有不同的分形特征。在收益率方面,根据MF-DFA方法测得的广义Hurst指数研究表明,中国股市大幅波动具有反持久性特征,小幅波动具有持久性特征,这表明了当市场发生大幅波动时,有较大的概率会改变原来的价格趋势,而发生小幅波动时,有较大的概率保持原来的趋势运行。在股价分布方面,通过运用多重分形谱的Holder指数、谱函数进行研究,发现样本时间内中国股价在较高价位和较低价位的奇异性程度不同,并且得出了这种奇异性的差异与股价总体的波动程度有关,当股价总体波动越大,高低价位的奇异性差距就越大；同时,谱函数的研究表明了样本时间内中国股价分布在低价位的概率较大,这是中国股市经历了2007年高峰后,长期低迷的真实写照。中国股市的单分形和多重分形特征表明了股票市场是一个复杂的、混沌的系统,在看似无序的市场中却存在着有序的特征,市场的价格变化是有规律可循的。因此,从理论上说,股价在一定程度上是可以预测的。那么在实践中,如何根据中国股市的分形特征找到有利于金融投资的有效信息,本文在此做了相关研究。将市场的单分形特征与金融投资相结合,根据市场长记忆性的突变特征,本文计算的短期移动Hurst指数和长期移动Hurst指数的运动规律中,可以找到指引未来股价走势的有效信息。这对于股市的投资实务有着重要的意义。另一方面,将市场的多重分形特征与金融投资相结合,通过对高频数据的研究发现,根据多重分形谱方法测度的市场Holder指数的差值△α可以作为衡量一天价格波动幅度的指标；同时,谱函数的差值△f可以作为一天股价分布方向、分布比例情况的指标。这对于金融投资过程中、尤其是量化投资中,对市场特征的量化提供了有力的参考工具。更进一步的,把中国股市单分形、多重分形特征相结合,以分形特征的量化指标为输入信息,运用滚动的神经网络模型对模拟股市的短期走势,发现可以取得了较好的预测效果,这对于股票市场的价格预测具有现实意义。
[Abstract]:Study on price behavior of stock market characteristics are widely concerned hot issues in academic and financial investment community. The effectiveness of random walk and the market price is an important theoretical foundation of mainstream finance theory. However, with the development of the market, the mainstream of the efficient market theory has been testing the actual operation situation of the market and related research. The fractal theory of Finance in physics as the research of financial market more appropriate tools, can greatly compensate for the lack of effective market theory. So this paper uses the fractal theory, the market characteristics of the December 16, 1996 to December 31, 2013 Shanghai stock index and Shenzhen stock index were studied from the multi fractal characteristics of single fractal feature and market the structure of the overall market to fully understand the market.
Study on single fractal feature of the China stock market shows that the stock market is a nonlinear system. The movement of stock prices is not consistent with the Brown motion and geometric Brown motion, in comparison, fractional Brown motion stock price fluctuations a better description. The distribution characteristics and yields, and can not use the normal distribution well described description returns distribution and fractal distribution with fat tail can be better. This shows that the fractal market to understand the stock market more in line with the actual situation. Overall, China stock market price has statistical self similarity and different time scales. The trend of similar morphology with distribution characteristics similar to the different time scales of the return rate. At the same time, R/S analysis showed that the China stock market is a non effective market, the market has long memory characteristics, before the price wave Dynamic and historical information will affect the stock price volatility, the stock price can be predicted to a certain extent. Further to the long memory cycle measurement showed that on average, the long memory of the Shanghai index will be reduced in 30 days, 70 days will disappear, the long memory of Shenzhen will be reduced in 30 days, 60 days will disappear.
Single fractal characteristics show that the overall characteristics of the market, further use of structural characteristics of multi fractal theory of market research showed that Chinese stock market is a multi fractal structure, between stock return rate fluctuation, have different fractal characteristics and the distribution of shares between the high and low price. In return, according to a study the generalized Hurst index measured by MF-DFA method, China stock market volatility has anti persistent characteristics, small fluctuations in durable characteristics, this shows that when the market volatility, there is a greater probability will change the price trend of the original, and the occurrence of small fluctuations, there is a greater probability to maintain the trend in running the original. The stock price distribution, by using the multi fractal spectrum of Holder index of spectrum function, found the sample time China shares at a high price and low price The singularity degree is different, and the degree of fluctuation difference of the singularity and the overall price, when the stock price fluctuation is the overall price level, the singularity of the gap is bigger; at the same time, the research shows that the spectrum of sample time China stock distribution in large probability of low price, this is Chinese stock market experience the peak in 2007, a true portrayal of a prolonged slump.
Single fractal and multi fractal characteristics of China stock market shows that the stock market is a complex, chaotic system, in the seemingly disorderly market but there are orderly characteristics, the market price changes is to follow the law. Therefore, theoretically, the stock price can be predicted to a certain extent so. In practice, according to the fractal characteristics of China stock market find useful information for financial investment, this paper has done the related research.
The fractal characteristics and the combination of financial markets, according to the mutation characteristics of the long memory of the market, this paper calculates the movement of short-term and long-term mobile mobile Hurst index Hurst index, the effective information can be found to guide the future stock price. This has important significance for the stock market investment practice. On the other hand, the multifractal characteristics and financial markets combined, through the research on the high frequency data, according to the difference between the alpha delta method to measure the multifractal spectrum of the market Holder index could be used to measure the day price volatility index; at the same time, the difference spectrum function f can be used as a day stock price distribution, distribution ratio the index for financial investment. This process, especially quantitative investment, to quantify the characteristics of the market provides a powerful reference tool. Further, the China single stock market Combining fractal and multi fractal characteristics, we use fractal quantitative index as input information and use rolling neural network model to simulate short-term trend of stock market. We find that it can achieve better prediction effect, which has practical significance for price prediction of stock market.

【学位授予单位】：安徽大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：F832.51

【参考文献】