股市波动性网络及其应用

发布时间：2018-10-19 15:49

【摘要】：股票市场的波动性问题一直以来都是国内外学者研究的热点，波动性理论研究比较成熟。近年来，复杂网络理论的应用越来越广泛，理论及实证研究丰富，发展迅速。在证券市场被证明是一个复杂系统以后，复杂网络在金融市场方面的应用研究也发展起来，开始在微观层面的基础上讨论股市的整体特征和性质。本文首先考察了目前不同学科领域中有关相似问题，并对其进行了深入地探讨及分析，归纳出描述两个对象相似的本质特征。针对复杂网络的特点，给出了复杂网络相似元的定义，利用向量的相关性和随机变量的相关系数等计量方法来计算相似元数值。在此基础上，重新给出复杂网络相似的定义并从微观层面和中观层面阐述和对比分析了几支股票指数之间及个股的相似性和自相似性，为研究复杂网络的自相似性研究提供一个新的视角。本文主要内容分三个部分，具体如下：第一部分主要是介绍股市波动性网络研究所需的背景和理论知识，包括股市波动性网络的研究现状，复杂网络的基本理论、股票市场的相关知识。第二部分重点介绍了目前各学科关于相似性、自相似性的描述，总结归纳相似的共同特征，给出复杂网络相似元、相似和自相似的定义及复杂网络相似元数值和相似度的计算方法，这为更好地理解复杂网络和复杂网络自相似性实际运用提供一个有力的分析工具。第三部分运用粗粒化方法建立复杂网络模型，基于点频率、点平均周期等概念，分析网络的重要拓扑特性和统计特性。然后对股指不同时间段的波动性网络的相似性和自相似性以及个股之间和股指之间同一时间段的波动性网络的相似性进行比较分析，说明不同地区和不同时间段的股市波动性网络之间的联系。在此基础上考虑个股波动性网络的性质。
[Abstract]:Volatility in stock market has always been a hot topic for scholars at home and abroad, and the theory of volatility is relatively mature. In recent years, the application of complex network theory is more and more extensive. After the securities market has been proved to be a complex system, the application of complex network in the financial market has also developed, and the overall characteristics and properties of the stock market have been discussed on the basis of the microscopic level. In this paper, we first investigate the similarity problems in different disciplines, and analyze them deeply, and conclude the essential characteristics of describing the similarity between the two objects. According to the characteristics of complex network, the definition of similarity element of complex network is given, and the similarity element value is calculated by using the methods of vector correlation and correlation coefficient of random variables. On this basis, the definition of similarity of complex network is redefined, and the similarity and self-similarity of several stock indices and individual stocks are analyzed and compared from the micro level and the middle level. It provides a new perspective for the study of self-similarity of complex networks. The main contents of this paper are as follows: the first part mainly introduces the background and theoretical knowledge needed for the research of volatility network in stock market, including the current research situation of volatility network in stock market, the basic theory of complex network, Knowledge of the stock market. The second part focuses on the description of similarity and self-similarity in various disciplines, summarizes the common characteristics of similarity, and gives the similarity element of complex network. The definition of similarity and self-similarity and the calculation method of similarity element and similarity degree of complex network provide a powerful tool for understanding the practical application of complex network and complex network self-similarity. In the third part, the rough granulation method is used to establish the complex network model. Based on the concepts of point frequency and point average period, the important topological and statistical characteristics of the network are analyzed. Then the similarity and self-similarity of volatility networks in different time periods of stock index and the similarity of volatility networks between individual stocks and stock indexes in the same time period are compared and analyzed. It shows the relationship between the stock market volatility network in different regions and different time periods. On this basis, consider the nature of the volatility network of individual stocks.
【学位授予单位】：华南理工大学
【学位级别】：硕士
【学位授予年份】：2012
【分类号】：F224;F830.91

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