证券市场价格系统复杂性及仿真研究
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摘要
证券市场价格系统的复杂性研究一直是学术界探讨的热点。本文在复杂性理论的框架下,提出新的市场分析范式。在新的分析范式下,以中国证券市场(上海证券市场和深圳证券市场)为实例,利用混沌、分形和类zipf分析法,从宏观层面研究了中国证券市场综合指数价格行为的复杂性特征。通过对真实证券市场进行抽象和映射,构建了虚拟证券市场仿真系统。使用新的市场分析范式对虚拟证券市场生成的价格时间序列进行分析,验证了虚拟证券市场的有效性。将虚拟证券市场的特征映射到真实证券市场,探求造成真实证券市场价格行为复杂性的内在微观机理。本文的创新性成果主要包括以下几个方面:
第一,引入混沌理论中相空间重构法、G-P算法、Wolf算法,分别考察了上海和深圳证券市场综合指数时间序列的混沌特征量,计算了两个市场综合指数的分维数、最大Lyapunov指数和Kolmogorov熵,判断出两个市场的综合指数系统是具有混沌和分形特征的复杂系统;
第二,引入分形市场假说的R/S分析法,进一步探讨了上海和深圳证券市场综合指数系统的分形特征。通过计算两个市场综合指数时间序列在不同时延下的Hurst指数,分析了两个市场综合指数系统具有长期记忆,深入分析并比较了两个证券市场内在的风险,并通过Ⅴ统计量得到两个市场综合指数的长期记忆周期;
第三,引入类Zipf分析法,将上海和深圳证券市场综合指数时间序列映射为代表价格上涨、平盘和下跌的3字母时间序列,分析3个字母各自对应持股周期的统计数据,得到价格波动的绝对和相对变化率,进而得出证券市场价格波动行为与市场参与者交易行为之间的对应关系;
第四,利用基于多智能体建模技术,对真实证券市场进行抽象,构建出虚拟证券市场仿真系统,通过观察虚拟证券市场价格波动的现象和其时间序列复杂性的分析结果,判断虚拟证券市场能有效的模拟真实市场的价格行为。根据多智能体的计算经济学中的二次映射机制,将虚拟证券市场价格复杂性的微观机理映射到真实证券市场,探寻造成证券市场价格系统行为复杂性的微观机理。
总之,利用新的复杂性分析范式可以得到证券市场价格系统的复杂性特征,通过基于多智能体建模分析技术不但能对传统经济学难以建模、难以定量研究的问题进行讨论;甚至可以探讨传统方法没有涉及的新领域。
The study of the complexity of security market price system has been the research direction. With the frame of system theory and complexity science, the dissertation presents a new pattern to analysis security market price system. This dissertation shows the complexity of price behavior of Chinese Security Market Composite Index from a macro-level by using methods such as chaos, fractal and Zipf-type analysis method. And a virtual security market system has been built by mapping the features of real market. Virtual security market system has been proved effective by analyze of the price time sequence produced by the virtual system. The micro-mechanisms of real market price behaviors were detected by mapping the virtual security market features to real market. The innovative points of the dissertation include four aspects:
Firstly, this dissertation observed the chaos characteristic quantities of Shanghai and Shenzhen Security Market Composite Index time sequence by applying the Phase Space Reconstruction Technique, G-P algorithm and Wolf algorithm. Non-integer correlation dimensions, largest Lyapunov exponents and Kolmogorov entropies of the two markets were obtained. According to the rules of judgment, the existence of chaos and fractal in above two systems was identified.
Secondly, the Rescaled Range analysis method was applied to investigate the fractal behaviors from the prices of Shanghai and Shenzhen Security Market Composite Index time sequence. The Hurst exponents of the two systems were estimated with the different time scales. The results have implied that the systems have positive persistency and fractal features. Furthermore, long-term memory effects and a serials period of non-period cycles were discovered by using V statistics.
Thirdly, based on Zipf-type analysis method, the time sequences of Shanghai and Shenzhen Security Market Composite Index were mapped and converted into 3-charactered sequences, which containing the fundamental information of price fluctuations (up, down and no-change). According to the statistic results of 3 characters, the rates of absolute and relative price changes of two markets were applied to build a link between price fluctuations and investors' trading behaviors.
Fourthly, based on Multi-Agent skills, a simulation stock market system was built with the simplest consumptions abstracted from real security market. The complex behaviors and phenomena were found from the data produced by the simulation stock market system. It means that the simulation system were effective to simulate the price mechanisms of real market. According to two phases of mapping mechanism of Multi-Agent based Computational Economics, those consumptions were mapped into real market for detecting the micro-mechanisms of real market complex price behaviors.
In summary, with the help of new complex analyze pattern; this dissertation has observed the complex features of security market. Multi-Agent method not only supports and verifies the traditional conclusions, but also manages to deal with tough problems that traditional methods can't analyze and even might able to penetrate into untouched areas.
第一,引入混沌理论中相空间重构法、G-P算法、Wolf算法,分别考察了上海和深圳证券市场综合指数时间序列的混沌特征量,计算了两个市场综合指数的分维数、最大Lyapunov指数和Kolmogorov熵,判断出两个市场的综合指数系统是具有混沌和分形特征的复杂系统;
第二,引入分形市场假说的R/S分析法,进一步探讨了上海和深圳证券市场综合指数系统的分形特征。通过计算两个市场综合指数时间序列在不同时延下的Hurst指数,分析了两个市场综合指数系统具有长期记忆,深入分析并比较了两个证券市场内在的风险,并通过Ⅴ统计量得到两个市场综合指数的长期记忆周期;
第三,引入类Zipf分析法,将上海和深圳证券市场综合指数时间序列映射为代表价格上涨、平盘和下跌的3字母时间序列,分析3个字母各自对应持股周期的统计数据,得到价格波动的绝对和相对变化率,进而得出证券市场价格波动行为与市场参与者交易行为之间的对应关系;
第四,利用基于多智能体建模技术,对真实证券市场进行抽象,构建出虚拟证券市场仿真系统,通过观察虚拟证券市场价格波动的现象和其时间序列复杂性的分析结果,判断虚拟证券市场能有效的模拟真实市场的价格行为。根据多智能体的计算经济学中的二次映射机制,将虚拟证券市场价格复杂性的微观机理映射到真实证券市场,探寻造成证券市场价格系统行为复杂性的微观机理。
总之,利用新的复杂性分析范式可以得到证券市场价格系统的复杂性特征,通过基于多智能体建模分析技术不但能对传统经济学难以建模、难以定量研究的问题进行讨论;甚至可以探讨传统方法没有涉及的新领域。
The study of the complexity of security market price system has been the research direction. With the frame of system theory and complexity science, the dissertation presents a new pattern to analysis security market price system. This dissertation shows the complexity of price behavior of Chinese Security Market Composite Index from a macro-level by using methods such as chaos, fractal and Zipf-type analysis method. And a virtual security market system has been built by mapping the features of real market. Virtual security market system has been proved effective by analyze of the price time sequence produced by the virtual system. The micro-mechanisms of real market price behaviors were detected by mapping the virtual security market features to real market. The innovative points of the dissertation include four aspects:
Firstly, this dissertation observed the chaos characteristic quantities of Shanghai and Shenzhen Security Market Composite Index time sequence by applying the Phase Space Reconstruction Technique, G-P algorithm and Wolf algorithm. Non-integer correlation dimensions, largest Lyapunov exponents and Kolmogorov entropies of the two markets were obtained. According to the rules of judgment, the existence of chaos and fractal in above two systems was identified.
Secondly, the Rescaled Range analysis method was applied to investigate the fractal behaviors from the prices of Shanghai and Shenzhen Security Market Composite Index time sequence. The Hurst exponents of the two systems were estimated with the different time scales. The results have implied that the systems have positive persistency and fractal features. Furthermore, long-term memory effects and a serials period of non-period cycles were discovered by using V statistics.
Thirdly, based on Zipf-type analysis method, the time sequences of Shanghai and Shenzhen Security Market Composite Index were mapped and converted into 3-charactered sequences, which containing the fundamental information of price fluctuations (up, down and no-change). According to the statistic results of 3 characters, the rates of absolute and relative price changes of two markets were applied to build a link between price fluctuations and investors' trading behaviors.
Fourthly, based on Multi-Agent skills, a simulation stock market system was built with the simplest consumptions abstracted from real security market. The complex behaviors and phenomena were found from the data produced by the simulation stock market system. It means that the simulation system were effective to simulate the price mechanisms of real market. According to two phases of mapping mechanism of Multi-Agent based Computational Economics, those consumptions were mapped into real market for detecting the micro-mechanisms of real market complex price behaviors.
In summary, with the help of new complex analyze pattern; this dissertation has observed the complex features of security market. Multi-Agent method not only supports and verifies the traditional conclusions, but also manages to deal with tough problems that traditional methods can't analyze and even might able to penetrate into untouched areas.
引文
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