数据驱动的股指收益率与波动率的预测方法研究

发布时间：2018-03-04 07:15

本文选题：金融预测　切入点：统计回归　出处：《合肥工业大学》2014年博士论文　论文类型：学位论文

【摘要】：我国的股票市场还处在成长阶段,因此有着其固有的特殊性。由于股市的不规范所带来的各种虚假信息,更是让投资者对股票价格的走向难以进行判断,从而损失许多利益。因此在金融市场中,特别是股票市场中,通过数据的分析及处理来探讨其内在的运行规律刻不容缓。而股票价格波动的背后定然存在着一些潜在的必然规律,且这些规律来调配股票的价格。因此,问题的焦点就集中在如何去寻找这些潜在的规律,这才是目前需要进行进一步去研究和探讨的重点。近些年,基于数据处理和分析的预测理论在金融市场发挥的作用越发明显,通过本文的具体研究,可以有效地运用数学模型将信息进行数学化的描述和分析,体现数据的变化趋势,挖掘潜在的固有规律等重要信息,从而为管理者以及投资者提供可靠的依据。本文运用数值分析理论、统计回归理论、智能优化理论等来解决金融领域的预测问题。从形式上说是给出了解决金融领域的问题的三类方法体系,从本质上理解,则是选取三个不同视角为切入点解决金融领域的预测。即数值分析理论主要解决预测过程中的计算过程的复杂性,统计回归理论聚焦消除预测过程中的影响变量的多重性,智能优化理论重点针对预测过程中的模型参数的优化性。在不同的金融数据类型下,采用不同的模型体系,只有“因人而异”才可以起到“药到病除”的效果。在具体的研究中,本文在简要地分析数据分析理论对促进科学预测的重要性,阐述科学预测在金融业,特别是股票市场中的重要性和必要性,以及论述金融预测模型的研究的国内外现状及其存在的问题的基础上,把灰色预测模型,偏最小二乘回归预测模型,时间序列预测模型和智能优化预测模型应用到金融领域的实践中去。本文的具体研究内容和创新性工作如下：一、在已有的传统灰色模型基础上,提出利用强化和弱化缓冲算子对原始数据序列进行数据进行预处理的策略,从而得到一组较为平缓的数据序列用于GM(1,1)预测模型的输入,然后分别利用组合插值和三次样条插值对传统GM(1,1)模型的背景值进行改进,以获得新的预测模型。最后利用本章的预测方法对上证指数日收益率进行仿真实验,结果表明,本章方法克服了受冲击扰动数据影响的问题,并且具有更高的模拟和预测精度。二、在William Sharpe提出的资本资产定价模型(CAPM)基础上,提出在多因子情况下遇到多重共线性问题时,一种新的解决这种困难的方法,即偏最小二乘的二次多项式回归方法。该方法不仅考虑每个因素对收益的影响,还可以考虑到影响因素之间的相互作用对收益的影响,从而更加全面的分析影响资产回报率的因素。另外,我们还把偏最小二乘支持回归理论与支持向量回归理论结合,解决中国股票市场的多影响因子的优化问题,克服各因子间的多重共线性的干扰,从而筛选出影响股票收益回报率的重要因素变量,为股市的技术分析提供一个可信的工具。三、考虑到SVR的算法过程中的由于不敏感损失函数中的ε、惩罚因子C和径向基函数中的σ2这三个参数取值的不同,则会导致支持向量回归模型不同的。故而在支持向量回归的理论基础上,结合我国经济运行的基本特点,汲取支持向量回归和群智能算法的优点,分别提出通过控制误差ε的取值,对偏最小二乘支持向量回归模型中参数集(C,σ2)采用带有RBF核的遗传算法进行近似寻优,之后采用偏最小二乘支持向量回归对上证综指收益率进行预测,算法对存在高度的非线性、耦合性的金融数据,有着良好的适应性,从而确保了预测的精度。四、针对金融数据的非线性和不确定等特性,借助模糊逻辑系统,提出一种新的金融市场波动率的预测方法-模糊FEGARCH模型,用来更好的应对具有非线性特性的收益率数据进行预测。其次,为了判断分布型模型和不对称型模型对预测精度的影响程度,分别采用分布型和不对称型与模糊FEGARCH)的波动模型进行预测比较。另外,综合智能算法和时间序列的优点对股票波动率进行预测,利用加权最小二乘支持向量回归模型进行初步预测,然后利用EGARCH模型对加权最小二乘支持向量回归的预测误差后进行修正,通过EGARCH模型来估计预测模型的拟合误差及其分布规律,得到最终的上证综指波动率预测值。最后,对上述两种方法的预测结果的采用的SPA检验方法,该方法的优点在于可以遍历对比每个模型的所有损失函数(预测误差),从而全面的比较模型的预测精度。
[Abstract]:China's stock market is still in the growth stage, so it has its inherent particularity. Because of all kinds of false information about the stock market is not standardized, more is to allow investors to the stock price is difficult to judge, to lose a lot of benefits. Therefore in the financial market, especially the stock market, through the analysis of data processing and to explore the internal rules and delay. The fluctuation of the stock price behind there are certainly some potential inevitable, and these rules to adjust the stock price. Therefore, the focus of the problem is focused on how to find the potential rules, this is the need to focus on further research and discussion. In recent years, based on the forecast theory of data processing and analysis of the play in the financial markets are becoming more and more important, through the research of this thesis, can effectively use the mathematical model The information is mathematically described and analyzed, reflecting the trend of data change and mining potential inherent laws and other important information, so as to provide reliable basis for managers and investors.
This paper uses numerical analysis theory, statistical regression theory, intelligent optimization theory to solve the prediction problem in the financial field. From the form that is given three kinds of methods to solve the financial problems in the field of system, understanding from the essence, it is from three different perspectives to solve the financial sector forecast as the starting point. The complexity of calculation the numerical analysis theory mainly solves the problem in the process of prediction, statistical regression theory predicts multiple variable focus elimination effect in process optimization, intelligent optimization theory focuses on the model parameters in the process of prediction. In the financial data of different types, using various model system, only the "It differs from man to man. can play" the "charm" effect. In the study, based on the brief analysis of data analysis theory to promote the importance of scientific prediction, expounds the scientific prediction in Finance Industry, especially the importance and necessity of the stock market in the foundation as well as the present situation and the existing problems of the model research of financial prediction discussed at home and abroad on the grey prediction model, partial least squares regression model, time series prediction model and intelligent optimization prediction model is applied to practice in the financial field.
The specific research content and innovative work of this paper are as follows:
A, the traditional grey model on the basis of the strengthening and weakening buffer operator of original data sequence of data pretreatment method, to obtain a set of relatively flat data sequence for GM (1,1) prediction model of the input, and then use the combination of interpolation and three spline interpolation on the traditional GM (1,1) improved the value model of the background, in order to obtain a new prediction model. Finally the prediction method of this chapter carries on the simulation experiment, the results show that the Shanghai Composite Index daily return rate, this chapter method overcomes the disturbance data affected by the impact, and has higher precision of prediction and simulation.
Two, the capital asset pricing model proposed by William Sharpe (CAPM) on the basis of this encounter the problem of multicollinearity in multi factor conditions, a new method of solving the problems, two polynomial regression method and partial least squares. This method not only influence each factor on income consideration, can also be considering the influence of the interaction between the influencing factors of income, thus a more comprehensive analysis of the impact of asset return factors. In addition, we also put the partial least squares regression and support vector regression theory of support theory combined with solving multi factor optimization problem China stock market, overcome the multicollinearity of the factors in order to find out the influence of variable interference, important factors of stock returns, providing a reliable tool for the analysis of the stock market.
Three, taking into account the algorithm in the process of SVR due to the insensitive loss function epsilon, penalty factor C and radial basis function in sigma 2 these three parameters will lead to different support vector regression model. Therefore based on the theory of support vector regression, combined with the basic characteristics of China's economy run, learn the advantages of support vector regression and swarm intelligence algorithm, are proposed through the values of control error epsilon, the partial least squares support vector regression model parameter sets (C, sigma 2) using genetic algorithm with RBF kernel approximation optimization, using partial least squares support vector regression on the returns of Shanghai composite index forecast after the algorithm of highly nonlinear, financial data coupling, has good adaptability, so as to ensure the accuracy of prediction.
Four, the financial data for the nonlinear and uncertain characteristics, by means of fuzzy logic system, put forward a kind of new financial market volatility rate prediction method of fuzzy FEGARCH model to yield data to better cope with the nonlinear prediction. Secondly, in order to judge the influence of distribution model and model of asymmetry the prediction accuracy, respectively by the distribution pattern and asymmetric type and fuzzy FEGARCH) of the wave model is compared. In addition, the comprehensive advantages of intelligent algorithms and the time series of stock volatility forecast, using weighted least squares support vector regression model to preliminary forecasts, then the prediction error of weighted least squares support vector regression after correction using EGARCH model to estimate the fitting error and prediction of the distribution of the model through the EGARCH model, the Shanghai Composite Index Fluctuation Finally, we use the SPA test method to predict the prediction results of the above two methods. The advantage of this method is that it can traverse all the loss functions of each model (prediction error), so as to comprehensively compare the prediction accuracy of the model.

【学位授予单位】：合肥工业大学
【学位级别】：博士
【学位授予年份】：2014
【分类号】：F832.51;F224

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