证券市场的长期记忆及聚类复杂性研究
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摘要
由于有效市场假说(EMH)存在正态分布假设与尖峰胖尾等问题，提出采用分形市场假说(FMH)，它不需要正态分布等假设条件。EMH所未能包含的长期记忆性，就是FMH的重要特征之一。长期记忆性也称长期相关性、长期依赖性，它描述了时间序列具有较长滞后期的相关性。如果一个时间序列存在长期记忆性，则相隔较长时期的观察值之间有着持续的相互依赖关系，此时的序列将会呈现出明显但又不定周期的循环波动特征。长期记忆特征对于系统非线性结构的确定以及市场有效性的研究具有重要的意义。由于股票市场存在长期记忆性，系统内的元素之间的相互作用是复杂多变的，因此属于非线性复杂系统，提出引入具有准确拓扑序列的亚超度量空间方法研究股票市场的聚类性。
针对G7以及“金砖四国”股票市场日收益率以及波动序列是否具有长期记忆性的问题，提出分别运用非参数统计法(R/S，V/S)和半参数估计法(GPH，tapered GPH)进行评估。通过选择2001年1月4日至2009年3月31日的SSEC、HSI、NIKKEI225、S&P500、DJI、FTSE100、CAC40、DAX、BOVESPA、MIBTEL、TSX、RTX、BSE30日收益率及其波动性为研究对象，结果发现：SSEC、HSI、NIKKEI225、FTSE100、CAC40、DAX、BOVESPA、MIBTEL、TSX、RTX、BSE30股指的日收益率序列具有长期记忆性，而S&P500、DH股指不具有长期记忆性；上述股指的日收益率波动序列都具有长期记忆性。这在某种程度上，美国的纽约股票市场最有效(DJI的Hurst指数为0.4582，最接近0.5)，而中国的上海股票市场相对来说最低效(SSEC的Hurst指数高达0．6882)。
针对证券市场中传统聚类法的参数和指标多样化导致的划分结果迥异的不足，提出引入具有准确拓扑序列的亚超度量空间方法：首先，计算出股票间任意两个股价间的相关系数，并在此基础上计算出超度量空间的欧式距离；其次，利用克鲁斯卡尔(Kruskal)的最小生成树算法，构建出股价的亚超度量空间；最后，将亚超度量空间映射为指数分层结构，并使其可视化。
(1)通过对2005年7月至2007年12月的沪深300的日数据实证发现：①行业聚类风格最为突出，而参股聚类风格、事件聚类风格、现金流聚类风格和规模聚类风格在每半年的时间区间内独立分布。但缺少以现代农业与服务业为代表的行业风格特征；②在行业聚类风格中，工业始终是中心节点，这一结果从新的视角证明了第二产业在中国宏观经济中极其重要的主导地位；③金融和电信处于指数分层结构的最高层次，是整个沪深300行业结构的稳固基础。这表明中国行业结构变化具有路径依赖性；④沪深300行业间的动态稳定性在整体上是相对稳定的，但在个别(如股改)时段产生了剧烈波动,这与当时的外部冲击改革政策有关。因此为了避免股市剧烈波动,股市的制度改革应该是渐进的;同时应加快推进第一、三产业中的行业领先者的企业优先上市。
(2)为了考察金融危机影响下全球股指的关联特征变化及动态稳定性,通过对2005年1月至2009年6月全球最具代表性的62个股指的日数据,进行金融危机前后对比实证,结果发现:金融危机爆发后,全球股市股指间地理区域聚类效应更加明显;股间距离明显缩短,各股指间的相关程度显著提高,其联动性更强;全球股市的动态稳定性在整体上是相对稳定的,但自2007年3月以来稳定性大幅减弱,这与全球金融危机的爆发有直接关系。为了避免股市剧烈波动,要及时制定合理的金融监管政策来防范金融风险,并且金融监管应该是全球协调,而不应是一个国家或某个区域的单独行为。保持各类金融机构的“多样性(差别化)”,来防止经济和金融一体化带来的“一荣俱荣,一损俱损!”。
上述结果表明亚超度量空间方法引入到证券市场的聚类研究中是有效的。
As the Efficient Market Hypothesis (EMH) assumed that the existence of a normal distribution, skewed or fat-tailed and other issues.Fractal Market Hypothesis (FMH) is proposed, it does not require assumptions such as normal distribution. EMH by the failure to include long-term memory is one of the important characteristics of FMH. Also known as long-term memory and long-term relationship, long-term dependence, which describes the time-series with a longer lag period related to each other. If the existence of a time series of long-term memory, then a longer period of observation between the value of the interdependence between the continuing relationship between the sequence at this time but will show a clear cycle of volatile fluctuations in the characteristics of the cycle.Characteristics of long-term memory for the system to identify non-linear structure, as well as the effectiveness of market research is of great significance. The existence of long-term memory as a result of the stock market, and the elements of the system is the interaction between the complex and changeable, and therefore are non-linear complex systems. The introduction of topology subdominant ultra-metric space is proposed for clustering method of the stock market.
Aimed at the problem of whether long-term memory exists in daily return time series and Volatility series about G7 and BRIC stock market. Non-parametric statistics methods of (classical R/S, modified R/S, V/S) and semi-parametric estimation (standard GPH, tapered GPH) comparatively are adopted to evaluate. The sample is to use close price of daily return time series of G7 and BRIC stock market from Jan 4, 2001 to Mar 31, 2009. It detects the long-term memory effect in daily returns and volatilities of three typical measures of G7 and BRIC stock market. The following results: The following results: Firstly, The long-term memory exists in daily returns of SSEC, HIS, NIKKEI225, FTSE100, CAC40, DAX, BOVESPA, MIBTEL, TSX, RTX, BSE30. Secondly, the long-term memory exists in their volatilities of three typical measures. There is very important meaning for the system to identify non-linear structure, as well as the effectiveness of market research. Partly, New York stock market of USA is the most effective( H of DJI on 0.4582 is the closest 0.5); Shanghai stock market of China is the most inefficient(H of SSEC is Up to 0.6882).
This study's objective was to overcome the issue of the popular parameter analysis method, which would bring the diversity of results in clustering analysis of securities market. Subdominant ultra-metric space is provided with the exactly defined topology sequence. Firstly, based on the correlation coefficient between every two housing prices of two cities, Euclidean distance of ultra-metric space is calculated; Secondly, subdominant ultra-metric space of portfolio is constructed based on minimum spanning tree of Kruskal; Finally, index hierarchical structure is mapped from subdominant ultra-metric space and its visualization.
(1) Via date from sample of Shanghai and Shenzhen 300 Index from Jul, 2005 to Dec,2007, results is finding: ?The style effect is prominent, especially for the industry style, and the other styles, for example, the sharing style, the event style, the capital style and the size style are distributed independently in different periods; (2) According to the MST, central node is the industry, which proves that the industry is very important in the China's macro-economic from the new perspective. (3) The finance and IT are in the highest lever of index hierarchical structure, which proves that the finance and IT are the basis of structure. This shows that the evolution of Shanghai and Shenzhen 300 industrial associated with the path-dependent. Between Shanghai and Shenzhen 300 industry in the overall dynamic stability are relatively stable on, but at the individual time (Joint-stock reform) had a dramatic fluctuations. This is Associated with severe external shocks at the time of the reform policies. In order to avoid sharp fluctuations in the stock market, stock market reform should be gradual and preference IPO about dominator of calling among the first and third industry is post advanced.
(2) In order to study the evolution of linkages and the dynamic stability of the national index of Global Stock Market under the impact of Financial Crisis. Via date data from the most representative stock index, January, 2005 to June, 2009, result of demonstration is finding: There is more significant clustering effect in world stock market after the outbreak of Financial Crisis. Over time, the distance between the national indexes shows a trend of reducing, which indicates that the relevance of the national index is improving more significantly. The dynamic stability of the global stock market overall is relatively stable. However, since March 2007 it has been significantly weakened. In order to avoid sharp fluctuations in the stock market, financial supervision should be global coordination, and should not be a country or a region of isolated acts. Develop reasonable financial regulatory policies timely to guard against financial risks. Maintain the diversity of all types of financial institutions, to prevent economic and financial integration of the saying" One with all, a loss will also be ruined!"
This shows that method of Subdominant Ultra-metric Space is effective in clustering analysis of securities market.
针对G7以及“金砖四国”股票市场日收益率以及波动序列是否具有长期记忆性的问题，提出分别运用非参数统计法(R/S，V/S)和半参数估计法(GPH，tapered GPH)进行评估。通过选择2001年1月4日至2009年3月31日的SSEC、HSI、NIKKEI225、S&P500、DJI、FTSE100、CAC40、DAX、BOVESPA、MIBTEL、TSX、RTX、BSE30日收益率及其波动性为研究对象，结果发现：SSEC、HSI、NIKKEI225、FTSE100、CAC40、DAX、BOVESPA、MIBTEL、TSX、RTX、BSE30股指的日收益率序列具有长期记忆性，而S&P500、DH股指不具有长期记忆性；上述股指的日收益率波动序列都具有长期记忆性。这在某种程度上，美国的纽约股票市场最有效(DJI的Hurst指数为0.4582，最接近0.5)，而中国的上海股票市场相对来说最低效(SSEC的Hurst指数高达0．6882)。
针对证券市场中传统聚类法的参数和指标多样化导致的划分结果迥异的不足，提出引入具有准确拓扑序列的亚超度量空间方法：首先，计算出股票间任意两个股价间的相关系数，并在此基础上计算出超度量空间的欧式距离；其次，利用克鲁斯卡尔(Kruskal)的最小生成树算法，构建出股价的亚超度量空间；最后，将亚超度量空间映射为指数分层结构，并使其可视化。
(1)通过对2005年7月至2007年12月的沪深300的日数据实证发现：①行业聚类风格最为突出，而参股聚类风格、事件聚类风格、现金流聚类风格和规模聚类风格在每半年的时间区间内独立分布。但缺少以现代农业与服务业为代表的行业风格特征；②在行业聚类风格中，工业始终是中心节点，这一结果从新的视角证明了第二产业在中国宏观经济中极其重要的主导地位；③金融和电信处于指数分层结构的最高层次，是整个沪深300行业结构的稳固基础。这表明中国行业结构变化具有路径依赖性；④沪深300行业间的动态稳定性在整体上是相对稳定的，但在个别(如股改)时段产生了剧烈波动,这与当时的外部冲击改革政策有关。因此为了避免股市剧烈波动,股市的制度改革应该是渐进的;同时应加快推进第一、三产业中的行业领先者的企业优先上市。
(2)为了考察金融危机影响下全球股指的关联特征变化及动态稳定性,通过对2005年1月至2009年6月全球最具代表性的62个股指的日数据,进行金融危机前后对比实证,结果发现:金融危机爆发后,全球股市股指间地理区域聚类效应更加明显;股间距离明显缩短,各股指间的相关程度显著提高,其联动性更强;全球股市的动态稳定性在整体上是相对稳定的,但自2007年3月以来稳定性大幅减弱,这与全球金融危机的爆发有直接关系。为了避免股市剧烈波动,要及时制定合理的金融监管政策来防范金融风险,并且金融监管应该是全球协调,而不应是一个国家或某个区域的单独行为。保持各类金融机构的“多样性(差别化)”,来防止经济和金融一体化带来的“一荣俱荣,一损俱损!”。
上述结果表明亚超度量空间方法引入到证券市场的聚类研究中是有效的。
As the Efficient Market Hypothesis (EMH) assumed that the existence of a normal distribution, skewed or fat-tailed and other issues.Fractal Market Hypothesis (FMH) is proposed, it does not require assumptions such as normal distribution. EMH by the failure to include long-term memory is one of the important characteristics of FMH. Also known as long-term memory and long-term relationship, long-term dependence, which describes the time-series with a longer lag period related to each other. If the existence of a time series of long-term memory, then a longer period of observation between the value of the interdependence between the continuing relationship between the sequence at this time but will show a clear cycle of volatile fluctuations in the characteristics of the cycle.Characteristics of long-term memory for the system to identify non-linear structure, as well as the effectiveness of market research is of great significance. The existence of long-term memory as a result of the stock market, and the elements of the system is the interaction between the complex and changeable, and therefore are non-linear complex systems. The introduction of topology subdominant ultra-metric space is proposed for clustering method of the stock market.
Aimed at the problem of whether long-term memory exists in daily return time series and Volatility series about G7 and BRIC stock market. Non-parametric statistics methods of (classical R/S, modified R/S, V/S) and semi-parametric estimation (standard GPH, tapered GPH) comparatively are adopted to evaluate. The sample is to use close price of daily return time series of G7 and BRIC stock market from Jan 4, 2001 to Mar 31, 2009. It detects the long-term memory effect in daily returns and volatilities of three typical measures of G7 and BRIC stock market. The following results: The following results: Firstly, The long-term memory exists in daily returns of SSEC, HIS, NIKKEI225, FTSE100, CAC40, DAX, BOVESPA, MIBTEL, TSX, RTX, BSE30. Secondly, the long-term memory exists in their volatilities of three typical measures. There is very important meaning for the system to identify non-linear structure, as well as the effectiveness of market research. Partly, New York stock market of USA is the most effective( H of DJI on 0.4582 is the closest 0.5); Shanghai stock market of China is the most inefficient(H of SSEC is Up to 0.6882).
This study's objective was to overcome the issue of the popular parameter analysis method, which would bring the diversity of results in clustering analysis of securities market. Subdominant ultra-metric space is provided with the exactly defined topology sequence. Firstly, based on the correlation coefficient between every two housing prices of two cities, Euclidean distance of ultra-metric space is calculated; Secondly, subdominant ultra-metric space of portfolio is constructed based on minimum spanning tree of Kruskal; Finally, index hierarchical structure is mapped from subdominant ultra-metric space and its visualization.
(1) Via date from sample of Shanghai and Shenzhen 300 Index from Jul, 2005 to Dec,2007, results is finding: ?The style effect is prominent, especially for the industry style, and the other styles, for example, the sharing style, the event style, the capital style and the size style are distributed independently in different periods; (2) According to the MST, central node is the industry, which proves that the industry is very important in the China's macro-economic from the new perspective. (3) The finance and IT are in the highest lever of index hierarchical structure, which proves that the finance and IT are the basis of structure. This shows that the evolution of Shanghai and Shenzhen 300 industrial associated with the path-dependent. Between Shanghai and Shenzhen 300 industry in the overall dynamic stability are relatively stable on, but at the individual time (Joint-stock reform) had a dramatic fluctuations. This is Associated with severe external shocks at the time of the reform policies. In order to avoid sharp fluctuations in the stock market, stock market reform should be gradual and preference IPO about dominator of calling among the first and third industry is post advanced.
(2) In order to study the evolution of linkages and the dynamic stability of the national index of Global Stock Market under the impact of Financial Crisis. Via date data from the most representative stock index, January, 2005 to June, 2009, result of demonstration is finding: There is more significant clustering effect in world stock market after the outbreak of Financial Crisis. Over time, the distance between the national indexes shows a trend of reducing, which indicates that the relevance of the national index is improving more significantly. The dynamic stability of the global stock market overall is relatively stable. However, since March 2007 it has been significantly weakened. In order to avoid sharp fluctuations in the stock market, financial supervision should be global coordination, and should not be a country or a region of isolated acts. Develop reasonable financial regulatory policies timely to guard against financial risks. Maintain the diversity of all types of financial institutions, to prevent economic and financial integration of the saying" One with all, a loss will also be ruined!"
This shows that method of Subdominant Ultra-metric Space is effective in clustering analysis of securities market.
引文
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