统计金融模型及金融市场波动持续时间序列的研究

发布时间：2018-01-08 18:11

本文关键词：统计金融模型及金融市场波动持续时间序列的研究　出处：《北京交通大学》2017年博士论文　论文类型：学位论文

【摘要】：在信息化交流越来越紧密的背景下,金融数据的传播和储存也变得更加方便,但同时也伴随着大量无法解释的金融现象发生.因此很多交叉学科为了解释这些金融现象应运而生,其中就有金融学和物理学的交叉学科“金融物理学”.金融物理学是将金融市场看作一个复杂的动力系统,把其中的各种金融数据看作是物理实验数据,再运用物理学中的各种概念、方法和理论来研究金融市场通过自组织而涌现的宏观规律.其中利用统计物理模型来解释和构建金融市场的波动行为是它的一个研究方法,而接触交互作用系统是统计物理模型中的一种.本论文对紧邻接触交互作用系统理论进行了阐述,在此基础之上,结合金融股票和随机过程的理论知识,构造了统计金融模型,得到了股票价格的表达式.进一步地,我们将紧邻接触交互作用系统拓展到了有限程多色接触交互作用系统,同样得到了相应的统计金融模型.为了说明这些模型的合理性,我们对来自金融市场真实数据的收益率序列和模拟得到的模拟数据进行了比较分析,对它们的统计特征进行了研究,主要从两个方面进行:一是我们将着重研究有限程多色接触交互作用系统在金融统计中的应用,这是一个新的模型,我们需要从不同的统计分析方法上去验证它完善它;二是我们构造了一种可以计量波动的持续时间的新统计量,我们将在由上述模型得到的原始收益率序列的基础上,再运用该统计量得到对应的波动持续时间序列来进行各类统计分析.以上研究可以验证我们的模型和统计量是合理的且有意义的,从而可以为金融市场的研究提供一种可行的方案.全文的组织结构如下:第一章,介绍选题背景、国内外研究成果以及本文的主要研究内容.第二章,介绍两种统计物理模型,分别是紧邻接触交互作用系统和有限程多色接触交互作用系统.对于每一个统计物理模型,详细介绍了它们的理论基础和如何构造基于该模型的统计金融模型.由此得到了两个统计金融模型,分别称为接触交互作用金融模型以及有限程多色接触交互作用金融模型.第三章,着重对接触交互作用金融模型进行统计分析,并且介绍了一种计量波动的持续时间的新统计量.将两者结合起来,也就是说对接触交互作用金融模型的模拟收益率序列进行转换,将其变成对应的波动持续时间序列,再对该波动持续时间序列进行统计分析.我们选用了 Zipf分析和交叉相关性分析两种方法,同时将真实金融市场中的实际数据所对应的收益率序列也转换成波动持续时间序列来作对比分析.第四章,着重对有限程多色接触交互作用金融模型进行统计分析.因为这是一个全新的模型,首先,我们对该模型进行了基本统计分析,包括描述性统计分析、正态性检验以及概率密度分布.然后,我们选用了幂律分布分析、自相关性分析、多尺度熵(MSE)分析、综合多尺度交叉熵分析(CMSCE)的方法分别对其分布性、波动集簇性、复杂性、不同时性这四个统计特征进行了研究.同时我们也对真实金融市场中的实际数据所对应的收益率序列进行了同样的分析来验证新模型的合理性和可行性.第五章,着重对有限程多色接触交互作用金融模型的波动持续时间序列进行统计分析.我们选用了自相关性分析、Lempel-Ziv复杂性(LZC)分析以及多重分形去趋势波动分析(MFDFA)的方法分别对其波动集簇性、复杂性和多重分形性进行了研究.同样的,我们也对真实金融市场中的实际数据所对应的波动持续时间序列进行了对比讨论.第六章,本文的创新点及结论.
[Abstract]:In the information exchange more closely under the background of financial data transmission and storage has become more convenient, but also accompanied by the occurrence of financial phenomena cannot be explained. Therefore many disciplines in order to explain the financial phenomenon came into being, which is a cross disciplinary "finance and physics financial physics. Physics is financial the financial market as a complex dynamic system, the financial data which is considered as a physical experiment data, and then use a variety of concepts in physics, method and theory to study the financial market through self organization and macroscopic law emerged. The fluctuation behavior by statistical physics model to explain and construct the financial market is a research the contact and interaction system is a kind of statistical physics model. The interaction of adjacent theory into the system of contact The paper, on the basis of this, combining theoretical knowledge of financial stocks and stochastic process, the statistical model of financial structure, expression of stock price is obtained. Further, we will close the contact interaction system is extended to the finite range multi contact interaction system, also obtained the corresponding financial statistics to illustrate. The rationality of these models, we simulated data from real data of financial market returns and simulation results were compared and analyzed, the statistical characteristics are studied, mainly from two aspects: one is that we will focus on the application of finite range multicolor contact interaction system in the financial statistics, this is a new model, we need from different statistical analysis methods to verify it and perfect it; two, we construct a quantifiable fluctuation duration The new statistics, we will base rate sequence obtained by the model of the original income, then get the corresponding wave duration sequence for various statistical analysis using statistics. The above research can verify the model and statistics we are reasonable and meaningful, provides a feasible scheme to study for the financial market. The thesis is organized as follows: the first chapter introduces the background, main contents and research achievements at home and abroad in this paper. The second chapter introduces two kinds of statistical physics model, respectively, is close to the system with a finite range interaction and multi touch contact interaction system. For each of the statistical physics model. Details of their theoretical basis and how to construct the model based on the financial statistics model. The two financial statistics model, called the contact interaction The financial model and the finite range multicolor contact interaction financial model. The third chapter focuses on the contact interaction of financial model for statistical analysis, and introduces a new statistic duration of a measurement fluctuation. Combine the two, that is the interaction of the financial model returns the conversion of contact, will a corresponding volatility time series, to analyze the volatility time series. We use Zipf analysis and cross correlation analysis two methods, at the same time corresponding to the actual data in the financial market rate of return sequence is converted into wave duration sequence for comparative analysis. The fourth chapter the finite range multicolor contact interaction financial model for statistical analysis. Because this is a new model, first of all, we are the basic of the model system Statistical analysis, including descriptive statistical analysis, normality test and probability density distribution. Then, we use the analysis of power-law distribution, autocorrelation analysis, multi-scale entropy (MSE) analysis, a comprehensive analysis of multiscale cross entropy (CMSCE) method respectively and the distribution of wave, dynamic clustering, complexity. At the four statistical characteristics were studied. At the same time we have actual data on the real financial market in the return series of the same analysis to verify the rationality and feasibility of the new model. The fifth chapter carries on the statistical analysis on duration sequence interaction of financial model for finite range multicolor contact wave we used the auto correlation analysis, Lempel-Ziv complexity (LZC) analysis and multifractal detrended fluctuation analysis (MFDFA) method respectively and the volatility clustering, complexity and multifractal properties are studied. Similarly, we also compare the volatility time series corresponding to the real data in real financial market. The sixth chapter is the innovation and conclusion of this paper.

【学位授予单位】：北京交通大学
【学位级别】：博士
【学位授予年份】：2017
【分类号】：F224;F832.51

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