股票市场的混沌特征分析及其判定研究

发布时间：2018-06-02 22:24

本文选题：混沌 + 股票市场　；参考：《首都经济贸易大学》2012年硕士论文

【摘要】：混沌是一种看似不规则的运动，指的是一个确定性的非线性系统，无需任何额外的随机因素，都可出现类似随机的行为（内在随机性）。在计算机技术的应用普及以及新兴的交叉科学出现后，混沌科学的研究随着现代科学技术的突飞猛进而飞速发展的。在现代物质世界里，大到宇宙，小到基本粒子，处处都有混沌理论，这些基本物质也都受混沌理论支配。非线性动力系统中出现混沌现象的原因在于，其演化过程中物体总是以某种特定规则不断沿袭前阶段的运动轨迹及状态，由此出现了不可预期的不确定、非规则的效应。混沌现象的产生原因体现了混沌现象的三个基本特征，即内在随机性、初值敏感性及非规则的有序性。所谓“差之毫厘，失之千里”正是混沌现象的最佳批注。混沌现象，具体来说，特别是一个容易发生改变的对象或系统，在初始状态是非常简单的运动，但经过一定规则的不断变化后，产生的后果往往出人意料，这就是混沌的状态。然而，这样的混沌状态与普通的、毫无头绪的混乱状态是有很大区别的，经过长期、完整的分析后，我们能从中整理出一种或几种特定的规则。尽管混沌现象最初是用来解释自然现象的，但是在人文科学和社会领域中的混沌现象特别常见，这是因为人文科学和社会领域中的事物彼此之间存在较多的联系与限制。1985年初次在经济系统中发现混沌现象后，随着混沌理论与计算机技术的发展，越来越多的经济学家开始将混沌理论作为研究和讨论社会经济的工具，包括财政、货币金融在内的经济和管理方面的问题，特别是有关证券市场股价指数方面的研究格外引人注目。功率谱和关联维数是分别从定性和定量方面判别混沌特性的重要方法，笔者在前人研究的基础上，一方面，将文献中最广泛使用的几种股指数据预处理方法：日收益率方法、对数线性趋势消除法，同时引入统计学中常用的min-max标准化方法，通过从定性和定量两方面的方法来验证数据样本的混沌性，辨析这几种数据预处理方法对股票市场混沌判定的影响；另一方面，，基于相同的数据样本，分析比较了两种的时间延迟算法：C－C算法和互信息量方法对股票市场混沌判定的影响。本文是笔者对股票市场混沌判定研究的一个新的探索，文章重点放在了数据预处理方法的辨析以及目前最常用的两种时间延迟算法的研究及技术实现上。在文章的最后，对于已判定出混沌的股票市场，如何降低其混沌度及股指数据的自相关性，还原股价指数波动成为真正社会经济的晴雨表，将成为未来对股票市场混沌研究的一个重要方面。本文对股指混沌时间序列预处理分析研究，以及对混沌科学在股票市场中的应用研究有着积极的意义，能够为今后混沌理论在股票市场甚至其他复杂经济系统的应用研究提供一定的参考依据。
[Abstract]:Chaos is a kind of seemingly irregular motion, which refers to a deterministic nonlinear system. Without any additional random factors, the behavior of chaos can be similar to that of random (intrinsic randomness). With the popularization of computer technology and the emergence of new cross-science, the research of chaotic science has developed rapidly with the rapid development of modern science and technology. In the modern material world, from the universe to the elementary particles, there are chaos theories everywhere, and these basic materials are also governed by the chaos theory. The reason for the chaos in nonlinear dynamic systems is that the objects always follow the track and state of the former stage with some special rules in the evolution process, which leads to the unpredictable and irregular effects. The causes of chaotic phenomena reflect the three basic characteristics of chaos, namely, intrinsic randomness, initial value sensitivity and irregularity. The so-called, "a thousand miles of loss" is the best endorsement of chaos. Chaos, especially an object or system that is prone to change, is a very simple motion in the initial state, but after a certain rule of continuous change, the consequences are often unexpected, this is the state of chaos. However, such a chaotic state is quite different from a general, clueless state of chaos. After a long and complete analysis, we can sort out one or more specific rules from it. Although chaos was originally used to explain natural phenomena, chaos is particularly common in the humanities and in the social sphere. This is because there are many connections and limitations between things in the humanities and social fields. After the first discovery of chaos in the economic system in 1985, with the development of chaos theory and computer technology, A growing number of economists are beginning to use chaos theory as a tool for studying and discussing socio-economic issues, including fiscal, monetary and financial issues, as well as economic and managerial issues. Especially on the stock market stock index research is particularly noticeable. Power spectrum and correlation dimension are important methods to judge chaotic characteristics from qualitative and quantitative aspects respectively. On the basis of previous studies, on the one hand, several widely used pre-processing methods of stock index data in literature: daily rate of return method are introduced. The logarithmic linear trend elimination method and the commonly used min-max standardization method in statistics are introduced to verify the chaos of data samples by qualitative and quantitative methods. On the other hand, based on the same data samples, this paper analyzes and compares the effects of two kinds of time delay algorithms, namely: C-C algorithm and mutual information method, on the chaos judgment of stock market. This paper is a new exploration for the study of chaos in the stock market. This paper focuses on the discrimination of data preprocessing methods and the research and technical implementation of the two most commonly used time delay algorithms at present. At the end of the paper, how to reduce the degree of chaos and the autocorrelation of stock index data to reduce the volatility of stock price index becomes the barometer of real social economy for the stock market that has been determined to be chaotic. It will become an important aspect of the future research on stock market chaos. This paper is of great significance to the research on the preprocessing of stock index chaotic time series and the application of chaotic science in stock market. It can provide some reference for the application of chaos theory in stock market and even other complicated economic systems in the future.
【学位授予单位】：首都经济贸易大学
【学位级别】：硕士
【学位授予年份】：2012
【分类号】：F224;F830.91

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