基于随机微分方程模型的金融时间序列预测的研究

发布时间：2018-05-13 03:29

本文选题：时间序列 + 随机微分方程　；参考：《济南大学》2012年硕士论文

【摘要】：伴随着经济的快速发展，金融市场日渐活跃。金融行业涉及社会生活的各个方面，对经济发展起着重要作用。越来越多的人加入股票市场、外汇市场、期货市场等进行投资，以期获得丰厚的经济利益。而在投资行为的推动下，越来越多的投资者开始意识到金融预测的重要性。时间序列分析是描述历史数据随时间的变化规律，可以用来预测经济数据，而金融时间序列不仅能为政府和投资机构提供参考，而且对企业和个人进行经营和风险管理都有重要意义，因此有关金融时间序列的分析和预测研究受到国内外学者的普遍关注。近年来产生了许多有关金融时序的预测模型，这些模型都在一定程度上说明了金融时间序列的短期发展趋势，例如：ARIMA模型、神经网络模型、支持向量机模型等，这些模型不仅有很好的适应能力，而且具有很高的预测精度。但是金融系统是一个复杂的、非线性的混沌动力系统，这是由其本身的运行机制引起的，因此应用以往的预测模型无法阐述金融市场存在各种干扰因素以及金融系统的混沌特征。随着现代数学的发展，微分方程系统应用于经济领域取得了很好的效果。本文提出随机微分方程模型，，即在微分方程基础上加入随机项，以获得金融系统的随机动力学描述，进而了解金融系统的内在运行规律。文中对随机微分方程采用差分化处理，避免了现代数学上还未解决的随机积分问题。本文在充分学习和研究进化算法的基础上，利用多表达式编程算法优化方程结构，利用遗传算法和粒子群优化算法进化方程的参数，文章最后以股票、汇率等金融时序预测的实证分析说明该模型的广泛适用性和较好的预测效果，并应用Matlab工具，通过图形对效果进行直观的感知。本文主要介绍了以下四方面的内容：（1）概述了时间序列的定义和性质及在日常生活中的应用，重点说明了已有的用于金融时序预测的模型特点和优缺点。（2）阐述了随机微分方程模型涉及的基础知识。着重介绍了金融时序的混沌特征，微分方程的概念、布朗运动的定义性质等一系列数学知识，以及将随机微分方程差分化处理的依据和方法。（3）概括介绍了进化算法、遗传编程的理论，引出多表达式编程算法，并详细论述了多表达式编程和遗传算法、粒子群优化算法的思想和实现流程。（4）将该模型应用于股票与汇率预测的实例中，主要包括：数据的采集和预处理、进化算法优化方程、利用Matlab工具进行误差分析等，由结论可知该模型的可行性和高效性。
[Abstract]:With the rapid development of economy, the financial market is becoming more and more active. The financial industry involves various aspects of social life and plays an important role in economic development. More and more people join the stock market, foreign exchange market, futures market and so on, in order to obtain rich economic benefits. Driven by investment behavior, more and more investors begin to realize the importance of financial forecasting. Time series analysis is to describe the law of historical data changing with time, and can be used to predict economic data, and financial time series can not only provide a reference for governments and investment agencies. Moreover, it is of great significance for enterprises and individuals to manage and manage risks. Therefore, the analysis and prediction of financial time series have been paid more and more attention by scholars at home and abroad. In recent years, there have been many forecasting models about financial time series. To some extent, these models illustrate the short-term development trend of financial time series, such as: Arima model, neural network model, support vector machine model, etc. These models not only have good adaptability, but also have high prediction accuracy. But the financial system is a complex, nonlinear chaotic dynamic system, which is caused by its own operating mechanism. Therefore, it is impossible to explain the financial market interference factors and the chaotic characteristics of the financial system by using the previous prediction model. With the development of modern mathematics, differential equation system has been applied to the field of economy. In this paper, a stochastic differential equation model is proposed, in which a random term is added to the differential equation to obtain the stochastic dynamic description of the financial system, and then to understand the inherent operating law of the financial system. In this paper, the stochastic differential equation is treated with difference, which avoids the unsolved stochastic integral problem in modern mathematics. On the basis of studying and studying the evolutionary algorithm, this paper optimizes the equation structure by using the multi-expression programming algorithm, and uses the genetic algorithm and particle swarm optimization algorithm to optimize the parameters of the evolution equation. The empirical analysis of financial time series forecasting, such as exchange rate, shows that the model has wide applicability and good forecasting effect, and the effect is intuitively perceived by using Matlab tool. This paper mainly introduces the following four aspects: 1) the definition and properties of time series and its application in daily life are summarized, and the characteristics, advantages and disadvantages of existing models for financial time series prediction are emphasized. The basic knowledge of stochastic differential equation model is expounded. The chaotic characteristics of financial time series, the concept of differential equation, the definition of Brownian motion and a series of mathematical knowledge are emphatically introduced, and the basis and method of differential treatment of stochastic differential equation are also discussed. 3) the evolutionary algorithm and the theory of genetic programming are introduced, and the multi-expression programming algorithm is introduced. The idea and realization flow of multi-expression programming and genetic algorithm and particle swarm optimization algorithm are discussed in detail. 4) the model is applied to stock and exchange rate forecasting examples, including data acquisition and preprocessing, evolutionary algorithm optimization equation, error analysis using Matlab tools, etc. The conclusion shows the feasibility and efficiency of the model.
【学位授予单位】：济南大学
【学位级别】：硕士
【学位授予年份】：2012
【分类号】：O211.61;F830;F224

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