基于多维泰勒网及其扩展的金融数据建模与预测研究

发布时间：2018-05-03 13:54

本文选题：动力学模型 + 多维泰勒网　；参考：《东南大学》2014年博士论文

【摘要】：金融系统是市场经济中市场资源合理配置机制的主导与枢纽,金融系统的正常运行是保证国家经济运行稳定的必要条件。金融数据包括股票价格,存贷款,基金,保险和外汇等,是经济数据中最重要的数据类型。对金融数据进行研究、分析和预测可以为国家宏观调控的制定做出指导方针。建立金融系统数学模型是研究金融系统的主要途径。现有基于金融系统运行机理的模型,主要针对具体金融领域展开,用以解决具体问题,但因金融系统结构复杂易变而存在局限性。基于非机理的数据建模方法,通过计算机的高速运转,可以快速处理大量金融数据,在金融数据分析中得到更广泛的应用,但是其存在仅关注数据内在联系而脱离实际的问题。为了建立更好的金融模型,使其为经济控制和国家宏观调控研究奠定基础,本文提出了基于多维泰勒网(MTN)的金融数据建模和预测方法,并进一步提出基于其扩展的动力学特性聚类多维泰勒网(DCMTN)、间歇反馈多维泰勒网(IFB-MTN)和带间歇反馈的多重多维泰勒网(MIMTN)金融数据建模和预测方法。本文以金融系统数据建模为背景,针对不同的建模侧重点,提出了数学模型,给出了相应模型求解方法。论文主要工作概括如下：1.针对金融系统内部要素多,结构复杂的问题,建立基于数据的金融系统动力学模型。研究了一般动力学模型的形式,结合金融系统含有多维状态向量的特点和泰勒展开式的基本原理,提出了多维泰勒网动力学模型。证明了多维泰勒网模型表达式的合理性,明确了模型中加权项排列次序和递归表达式。通过共轭梯度法对模型参数的迭代求解,得到了多维泰勒网模型参数求解的一般方法。为了测试模型的有效性,先通过数据滤波和分解方法,减少金融数据中随机扰动带来的影响,然后对分解后的每个数据子集分别建立多维泰勒网模型、辨识其参数并进行预测,最后将预测结果叠加输出。仿真实验结果表明了模型及算法的有效性,也为基于多维泰勒网模型的扩展研究奠定基础。2.针对金融系统内部流动性快,结构和特性易变的特点,建立动力学特性随预测目标不同而改变的金融系统动力学预测模型。研究了金融系统的动力学特点,定义了动力学特性,并证明了其数学表达形式的合理性。根据金融数据中数据点的不同动力学特性相似程度,定义了动力学特性相似度的具体形式,总结归纳并证明了其拥有的性质。结合多维泰勒网和动力学特性及相似度,提出了基于动力学特性聚类多维泰勒网的金融系统动力学预测模型。通过最小二乘估计的方法辨识了模型的参数。实例结果表明,动力学特性聚类多维泰勒网模型是可行和有效的。3.针对金融系统因为羊群效应而波动的特点,建立基于数据辅以机理分析的金融系统动力学模型。研究了羊群效应的机理和形成原因,分析总结了其通过数据对外表征的波动形式,给出了间歇反馈的概念,通过正负方向带起止阈值的死区函数叠加描述了间歇反馈的具体数学表达式。证明了用间歇反馈描述系统状态控制量的可行性。结合多维泰勒网和间歇反馈,提出了间歇反馈多维泰勒网金融系统动力学模型及其参数辨识方法。应用实例通过对实际金融数据的建模验证了间歇反馈多维泰勒网模型的可行性,预测结果表明其优于传统非机理数据模型。4.针对间歇反馈多维泰勒网动力学模型中,模拟羊群效应的间歇反馈部分与多维泰勒网部分在进行系统辨识时辨识针对性不精确的问题,建立基于参数交替迭代的优化模型。为了平衡间歇反馈多维泰勒网动力学模型中两部分子模块的所占比重,通过对多维泰勒网特性的挖掘,构造了多重多维泰勒网(MMTN)的模型结构。证明了多重多维泰勒网可以适用于相同状态向量、不同目标输出的数据子集建模叠加。基于多重多维泰勒网的多重叠加性质,在间歇反馈多维泰勒网模型的基础上,提出了基于带间歇反馈的多重多维泰勒网金融系统动力学模型建模方法。给出了其参数辨识的具体方法。实例结果表明其预测效果好于传统非机理数据建模方法,同时也好于间歇反馈多维泰勒网动力学模型。
[Abstract]:The financial system is the leading and hub of the rational allocation mechanism of market resources in the market economy. The normal operation of the financial system is the necessary condition to ensure the stability of the country's economic operation. The financial data includes the stock price, the deposit and loan, the fund, the insurance and the foreign exchange. It is the most important data type in the economic data. And prediction can provide guidance for the formulation of national macro-control. The establishment of a mathematical model of the financial system is the main approach to the study of the financial system. The existing model based on the operational mechanism of the financial system is mainly aimed at specific financial fields to solve specific problems, but the constraints are limited because of the complex and changeable structure of the golden thaw system. The non mechanism data modeling method, through the high speed operation of the computer, can quickly process a large amount of financial data and get more extensive application in the financial data analysis, but its existence is only concerned with the internal connection of the data and divorced from the actual problems. In order to establish a better financial model, it makes it for economic control and national macro-control research. In this paper, we propose a method for modeling and prediction of financial data based on multidimensional Taylor network (MTN), and further propose a method for modeling and forecasting the financial data of the multidimensional Taylor network (DCMTN), intermittent feedback multidimensional Taylor net (IFB-MTN) and multiple multidimensional Taylor network (MIMTN) with intermittent feedback based on its extended dynamic characteristics. Based on the data modeling of the financial system, the mathematical model is proposed and the corresponding model solving method is given. The main work of this paper is summarized as follows: 1. in view of the problems in the internal elements of the financial system and the complex structure of the financial system, the dynamic model of the financial system based on the data is established. In the form, combining the characteristics of the multi-dimensional state vector in the financial system and the basic principle of Taylor expansion, a dynamic model of multidimensional Taylor net is proposed. The rationality of the multidimensional Taylor net model expression is proved, the order of weighted terms and the recursive expression in the model are clarified. The iterative solution of the model parameters by the conjugate gradient method is obtained. In order to test the validity of the model, in order to test the validity of the model, the effect of the random disturbance in the financial data is reduced by the method of data filtering and decomposition. Then, the multidimensional Taylor net model is established for each subset of the decomposed data, and the parameters are identified and predicted. Finally, the prediction results are made. The simulation experiment results show the validity of the model and algorithm. It also lays the foundation for the extended study based on the multi-dimensional Taylor network model. The dynamic characteristics of the financial system in the financial system are fast, the structure and characteristics are changeable, and the dynamic prediction model of the dynamic characteristics of the financial system with different prediction targets is established. The dynamic characteristics of the fusion system, the dynamic characteristics are defined, and the rationality of the mathematical expression is proved. According to the similarity degree of the dynamic characteristics of the data points in the financial data, the specific form of the similarity of the dynamic characteristics is defined. The characteristics of the similarity are summarized and proved, and the multidimensional Taylor network and the dynamic characteristics are combined. And similarity, a dynamic prediction model of financial system based on dynamic characteristic clustering multi-dimensional Taylor net is proposed. The parameters of the model are identified by the least square estimation method. The results show that the dynamic clustering multi-dimensional Taylor net model is a feasible and effective.3. for the volatility of the financial system because of the herd effect. The dynamic model of financial system based on data and mechanism analysis is established. The mechanism and causes of the herd effect are studied. The fluctuation form of its external representation is analyzed and summarized. The concept of intermittent feedback is given. The specific mathematical expression of intermittent feedback is described by the superposition of dead zone function with the threshold threshold of positive and negative direction. The feasibility of describing the state control of the system with intermittent feedback is proved. Combined with multidimensional Taylor network and intermittent feedback, the dynamic model and parameter identification method of the intermittent feedback multidimensional Taylor network financial system are proposed. The feasibility of the intermission feedback multidimensional Taylor net model is verified by the actual financial data modeling. The test results show that it is superior to the traditional non mechanism data model.4. for the batch feedback multidimensional Taylor network dynamic model. The batch feedback part of the herd effect and the multidimensional Taylor net part identify the problem of inaccuracy in the system identification, and the optimization model based on the alternate iteration of parameters is established. In order to balance the intermittent feedback, the model is used to balance the intermittent feedback. The proportion of two molecular modules in the dynamic model of multidimensional Taylor network is constructed by mining the properties of multidimensional Taylor network. It is proved that the multi dimensional Taylor net (MMTN) model can be applied to the same state vector, the data subset of different target output is superimposed. The multi dimensional Taylor network based on multiple multidimensional Taylor network is used. On the basis of intermittent feedback multidimensional Taylor network model, the modeling method of dynamic model of multi dimensional Taylor net financial system based on intermittent feedback is proposed. The specific method of parameter identification is given. The results show that the prediction effect is better than the traditional non mechanism data modeling method, and it is also better than intermittent inverse. The dynamic model of feed multidimensional Taylor net.

【学位授予单位】：东南大学
【学位级别】：博士
【学位授予年份】：2014
【分类号】：F830;N945.14

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