中国证券市场的多重分形及有效性研究
发布时间：2018-11-14 15:09
【摘要】：金融市场是一个非常复杂的非线性动态系统。伴随着非线性科学研究的迅猛发展,越来越多的学者运用分形市场理论对金融市场中价格波动的非线性现象进行了研究。已有的实证研究表明,金融市场呈现出复杂的多重分形特征。对多重分形理论进行系统的研究,有助于我们进一步加深对金融市场复杂性的认识,揭示出金融市场复杂行为的形成机理以及动态变化规律。 本文选取上海证券综合指数(简称上证综指)和深圳证券成份指数(简称深证成指)1995年1月23日至2012年3月1日的每日收盘价格的股指收益数据为样本。本文采用MFDMA方法对我国股市的多重分形特征、成因以及市场的有效性进行了实证研究。主要包括以下几个方面： (1)验证了两序列的多重分形特征,并提出了一种改进的指标Ah'和△α'来衡量其多重分形程度,从而很好的实现了序列多重分形特征强度的量化。 (2)分析了形成两序列多重分形的原因,通常认为多重分形主要来源于序列的长程相关性和分布的重尾性。比较流行的做法是分别利用置乱数据(suffling data)法和相位随机化的Fourier变换法来分析序列的长程相关性和分布的重尾性对多重分形的影响。然而相位随机化的Fourier变换法(FT)是将序列的非线性结构完全消除,而保持其线性相关性,这里的非线性性包括分布的非线性性(即重尾性)和动态的非线性性(即非线性相关性),这样利用相位随机化的Fourier变换法来分析分布的重尾性对多重分形的影响就不是很严谨。振幅调整的Fourier变换法(AAFT)能保持原序列的分布和线性相关性,而将非线性相关性去掉了,因此本文采用相位随机化的Fourier变换法以及振幅调整的Fourier变换法相结合的方法来判断分布的重尾性以及序列的非线性相关性对多重分形的影响。 结果显示,上证综指收益率序列的多重分形来源于分布的重尾性；而深证成指收益率序列的多重分形由序列的长程相关性和重尾分布性所致。两序列的多重分形均不受非线性相关性的影响。因此可以说中国股市的多重分形特征来源于序列的长程相关性和分布的重尾性,而非线性相关性对其没有影响。 (3)检测了上海证券市场和深圳证券市场的有效性,通常认为多重分形程度高则市场有效性程度低,这只是粗略的说法,为了更加准确的判断市场的有效性程度,本文利用多重分形情形下的有效性指标DME对上证综指和深证成指收益率序列的有效性进行了实证分析。结果显示上海证券市场的有效性程度高于深圳证券市场的有效性程度。
[Abstract]:Financial market is a very complex nonlinear dynamic system. With the rapid development of nonlinear science, more and more scholars use fractal market theory to study the nonlinear phenomenon of price fluctuation in financial market. The existing empirical studies show that the financial market presents complex multifractal characteristics. The systematic study of multifractal theory will help us to deepen our understanding of the complexity of financial market and reveal the formation mechanism and dynamic change law of complex behavior in financial market. This paper selects the Shanghai Composite Index (Shanghai Composite Index for short) and Shenzhen Securities component Index (Shenzhen Composite Index) as samples of the daily closing price from January 23, 1995 to March 1, 2012. This paper makes an empirical study on the multifractal characteristics, causes and efficiency of the stock market in China by using the MFDMA method. The main contents are as follows: (1) the multifractal characteristics of the two sequences are verified, and an improved index Ah' and 伪'is proposed to measure the multifractal degree. Thus, the quantization of multifractal feature strength of sequence is well realized. (2) the causes of multifractal of two sequences are analyzed. It is generally considered that multifractal mainly comes from the long range correlation of sequences and the heavy-tailed distribution. It is popular to use (suffling data) method of scrambling data and Fourier transform of phase randomization to analyze the influence of long range correlation and heavy-tailed distribution on multifractal. However, the phase randomization Fourier transform (FT) eliminates the nonlinear structure of the sequence completely and maintains its linear correlation. The nonlinearity here includes the nonlinearity of the distribution (that is, heavy-tailed property) and the dynamic nonlinearity (that is, the nonlinear correlation). Therefore, it is not very strict to use phase randomization Fourier transform to analyze the influence of heavy-tailed distribution on multifractal. The amplitude-adjusted Fourier transform method (AAFT) can keep the distribution of the original sequence and the linear correlation, but the nonlinear correlation is removed. In this paper, the method of phase randomization Fourier transform and amplitude-adjusted Fourier transform are used to judge the influence of the heavy-tailed distribution and the nonlinear correlation of the sequence on multifractal. The results show that the multifractal of the yield series of the Shanghai Composite Index comes from the heavy-tailed distribution, while the multifractal of the yield sequence of Shenzhen Composite Index is caused by the long range correlation and the heavy-tailed distribution of the series. The multifractal of two sequences is not affected by nonlinear correlation. Therefore, it can be said that the multifractal feature of Chinese stock market comes from the long range correlation of the series and the heavy-tailed distribution, but the nonlinear correlation has no effect on it. (3) the validity of Shanghai stock market and Shenzhen stock market is tested. It is generally considered that the degree of market efficiency is low if the multifractal degree is high. This is only a rough statement, in order to judge the validity degree of the market more accurately, In this paper, the validity of the return series of Shanghai Composite Index and Shenzhen Composite Index is empirically analyzed by using the validity index DME in the case of multifractal. The results show that the efficiency of Shanghai stock market is higher than that of Shenzhen stock market.
【学位授予单位】：山西大学
【学位级别】：硕士
【学位授予年份】：2012
【分类号】：F832.51;F224
本文编号：2331524
[Abstract]:Financial market is a very complex nonlinear dynamic system. With the rapid development of nonlinear science, more and more scholars use fractal market theory to study the nonlinear phenomenon of price fluctuation in financial market. The existing empirical studies show that the financial market presents complex multifractal characteristics. The systematic study of multifractal theory will help us to deepen our understanding of the complexity of financial market and reveal the formation mechanism and dynamic change law of complex behavior in financial market. This paper selects the Shanghai Composite Index (Shanghai Composite Index for short) and Shenzhen Securities component Index (Shenzhen Composite Index) as samples of the daily closing price from January 23, 1995 to March 1, 2012. This paper makes an empirical study on the multifractal characteristics, causes and efficiency of the stock market in China by using the MFDMA method. The main contents are as follows: (1) the multifractal characteristics of the two sequences are verified, and an improved index Ah' and 伪'is proposed to measure the multifractal degree. Thus, the quantization of multifractal feature strength of sequence is well realized. (2) the causes of multifractal of two sequences are analyzed. It is generally considered that multifractal mainly comes from the long range correlation of sequences and the heavy-tailed distribution. It is popular to use (suffling data) method of scrambling data and Fourier transform of phase randomization to analyze the influence of long range correlation and heavy-tailed distribution on multifractal. However, the phase randomization Fourier transform (FT) eliminates the nonlinear structure of the sequence completely and maintains its linear correlation. The nonlinearity here includes the nonlinearity of the distribution (that is, heavy-tailed property) and the dynamic nonlinearity (that is, the nonlinear correlation). Therefore, it is not very strict to use phase randomization Fourier transform to analyze the influence of heavy-tailed distribution on multifractal. The amplitude-adjusted Fourier transform method (AAFT) can keep the distribution of the original sequence and the linear correlation, but the nonlinear correlation is removed. In this paper, the method of phase randomization Fourier transform and amplitude-adjusted Fourier transform are used to judge the influence of the heavy-tailed distribution and the nonlinear correlation of the sequence on multifractal. The results show that the multifractal of the yield series of the Shanghai Composite Index comes from the heavy-tailed distribution, while the multifractal of the yield sequence of Shenzhen Composite Index is caused by the long range correlation and the heavy-tailed distribution of the series. The multifractal of two sequences is not affected by nonlinear correlation. Therefore, it can be said that the multifractal feature of Chinese stock market comes from the long range correlation of the series and the heavy-tailed distribution, but the nonlinear correlation has no effect on it. (3) the validity of Shanghai stock market and Shenzhen stock market is tested. It is generally considered that the degree of market efficiency is low if the multifractal degree is high. This is only a rough statement, in order to judge the validity degree of the market more accurately, In this paper, the validity of the return series of Shanghai Composite Index and Shenzhen Composite Index is empirically analyzed by using the validity index DME in the case of multifractal. The results show that the efficiency of Shanghai stock market is higher than that of Shenzhen stock market.
【学位授予单位】：山西大学
【学位级别】：硕士
【学位授予年份】：2012
【分类号】：F832.51;F224
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