数据驱动的股指收益率与波动率的预测方法研究
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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。
Data processing and analysis plays a very important role in the development of prediction theory. According to the forecast theory, we can use mathematical models to describe and analyze the information in order to reflect the trend of data. Tap the potential of natural law and other important information, so as to provide a reliable basis for decision makers. The theoretical prediction which is based on data processing and analysis plays a very important role in the financial markets. As is known to all, China's stock market is still in the growth stage, so it has the inherent particularity. As the stock market is not standardized, there are all kinds of false information.The investors is difficult to judge the stock price, so as to lose a lot of interest. Therefore, it is crunch time to use the data processing and analsis to explore the internal rules in the financial markets. It will exist some potential inevitable rules behind the volatility of the stock price, and these rules will control the stock price. Therefore, the focus is how to find the potential rules.
In this paper, we use numerical value analysis theory, statistical regression theory, and intelligent optimization theory to solve the problem of predicting in financial field. On the one hand, from the form, this paper gives three methods to solve the financial problems. On the other hand, understood from the essence, it is selected from three different perspectives as the breakthrough point to predict in the financial field. The numerical analysis theory is mainly to solve the computational complexity in prediction process, the statistical regression theory focused on eliminating the factor of multiplicity, and intelligent optimization theory focuses on the model parameters of optimization. With different types of financial data, the theory system is different. This paper has analyzed the importance of scientific predictions. Expound the scientific prediction of importance and necessity in the stock market. Based on the present study of financial prediction model at home and abroad and the existing problems, we appliy the grey prediction model, partial least squares regression model, time series prediction model and intelligent optimization prediction model to the financial field.
In this paper, the research content and innovation are as follows:
1. In the basis of traditional grey model, we use the strengthening and weakening buffer operator to preprocess the original data sequence. Then, we obtain a set of flat data sequence as the GM (1,1) prediction model of input values. We use a combination interpolation and three spline interpolations improve the traditional GM (1,1) model's background value. Then, we can obtain a new prediction model. Finally, we use prediction method of simulation experiment in the Shanghai Composite Index daily return rate. The results show that, the method overcomes the disturbance problem, and has a high simulation and prediction accuracy.
2. Based on the capital asset pricing model (CAPM), we propose a new method to solve the multicollinearity. The model is partial least squares and two polynomial regression methods. The method not only takes into account the effect of each factor on income, but also taking into account the effect of interaction between factors. It can comprehensive analysis of influencing factors of the return on equity. In addition, combined with partial least squares support regression theory and support vector regression theory, solve the multi factor optimization problem in Chinese stock market. The method can overcome the interference of Multicollinearity, so as to select the important factors of rate of return. Therefore, it is a reliable tool for the analysis of stock market.
3. TheShanghai Composite Index Return and financial industry related tax revenue is non-linear and coupled, and is influenced by many factors. Therefore, traditional forecasting methods are not sufficient to predict the value of it. In this paper, disadvantages of the existing forecasting methods are analyzed. Then partial least square support vector regression (PLS-SVR) is used to construct a tax revenue prediction model. The Genetic algorithm with RBF networkis used to optimize the parameter set of (C,σ2) andε, which influences the performance of this model directly. By doing so, this model can deal with the nonlinearity and ensure stability and accuracy of support vector machine based regression. Experimental results show that, the algorithm has a good adaptability to the financial data which is highly nonlinear and coupling.
4.In general, the transmission of volatility in the stock market is time-varying, nonlinear, and asymmetric with respect to both positive and negative results. Given this fact, we adopt the method of fuzzy logic systems to modify the threshold values for an EGARCH model. This study investigates the volatility forecasting for the SSEC stock index series and identifies the essential source of performance improvements between distributional assumption and volatility specification using distribution-type and asymmetry-typevolatility models through the superior predictive ability test. Such evidence strongly demonstrates that modeling asymmetric components which is the fuzzy EGARCH model is more important than specifying error distribution for improving volatility forecasts of financial returns in the presence of fat-tails, leptokurtosis, skewness, leverage effects and nonlinear effects in china stock market.In addition, we points out the deficiency of the existing methods. Based on them, the author renders WLS-SVR and the correlated mathematics modeling the errors of which are supposed as time series and the errors have auto-correlation between themselves.As a result, the paper supposed to use EGARCH model to mine the tendency information of the above errors. Then we use the result to modify predicted value of the volatility of stocks. Finally, we study a case with the satisfactory result by the SPA test which is showing that this model is more accurate than other models.
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。
Data processing and analysis plays a very important role in the development of prediction theory. According to the forecast theory, we can use mathematical models to describe and analyze the information in order to reflect the trend of data. Tap the potential of natural law and other important information, so as to provide a reliable basis for decision makers. The theoretical prediction which is based on data processing and analysis plays a very important role in the financial markets. As is known to all, China's stock market is still in the growth stage, so it has the inherent particularity. As the stock market is not standardized, there are all kinds of false information.The investors is difficult to judge the stock price, so as to lose a lot of interest. Therefore, it is crunch time to use the data processing and analsis to explore the internal rules in the financial markets. It will exist some potential inevitable rules behind the volatility of the stock price, and these rules will control the stock price. Therefore, the focus is how to find the potential rules.
In this paper, we use numerical value analysis theory, statistical regression theory, and intelligent optimization theory to solve the problem of predicting in financial field. On the one hand, from the form, this paper gives three methods to solve the financial problems. On the other hand, understood from the essence, it is selected from three different perspectives as the breakthrough point to predict in the financial field. The numerical analysis theory is mainly to solve the computational complexity in prediction process, the statistical regression theory focused on eliminating the factor of multiplicity, and intelligent optimization theory focuses on the model parameters of optimization. With different types of financial data, the theory system is different. This paper has analyzed the importance of scientific predictions. Expound the scientific prediction of importance and necessity in the stock market. Based on the present study of financial prediction model at home and abroad and the existing problems, we appliy the grey prediction model, partial least squares regression model, time series prediction model and intelligent optimization prediction model to the financial field.
In this paper, the research content and innovation are as follows:
1. In the basis of traditional grey model, we use the strengthening and weakening buffer operator to preprocess the original data sequence. Then, we obtain a set of flat data sequence as the GM (1,1) prediction model of input values. We use a combination interpolation and three spline interpolations improve the traditional GM (1,1) model's background value. Then, we can obtain a new prediction model. Finally, we use prediction method of simulation experiment in the Shanghai Composite Index daily return rate. The results show that, the method overcomes the disturbance problem, and has a high simulation and prediction accuracy.
2. Based on the capital asset pricing model (CAPM), we propose a new method to solve the multicollinearity. The model is partial least squares and two polynomial regression methods. The method not only takes into account the effect of each factor on income, but also taking into account the effect of interaction between factors. It can comprehensive analysis of influencing factors of the return on equity. In addition, combined with partial least squares support regression theory and support vector regression theory, solve the multi factor optimization problem in Chinese stock market. The method can overcome the interference of Multicollinearity, so as to select the important factors of rate of return. Therefore, it is a reliable tool for the analysis of stock market.
3. TheShanghai Composite Index Return and financial industry related tax revenue is non-linear and coupled, and is influenced by many factors. Therefore, traditional forecasting methods are not sufficient to predict the value of it. In this paper, disadvantages of the existing forecasting methods are analyzed. Then partial least square support vector regression (PLS-SVR) is used to construct a tax revenue prediction model. The Genetic algorithm with RBF networkis used to optimize the parameter set of (C,σ2) andε, which influences the performance of this model directly. By doing so, this model can deal with the nonlinearity and ensure stability and accuracy of support vector machine based regression. Experimental results show that, the algorithm has a good adaptability to the financial data which is highly nonlinear and coupling.
4.In general, the transmission of volatility in the stock market is time-varying, nonlinear, and asymmetric with respect to both positive and negative results. Given this fact, we adopt the method of fuzzy logic systems to modify the threshold values for an EGARCH model. This study investigates the volatility forecasting for the SSEC stock index series and identifies the essential source of performance improvements between distributional assumption and volatility specification using distribution-type and asymmetry-typevolatility models through the superior predictive ability test. Such evidence strongly demonstrates that modeling asymmetric components which is the fuzzy EGARCH model is more important than specifying error distribution for improving volatility forecasts of financial returns in the presence of fat-tails, leptokurtosis, skewness, leverage effects and nonlinear effects in china stock market.In addition, we points out the deficiency of the existing methods. Based on them, the author renders WLS-SVR and the correlated mathematics modeling the errors of which are supposed as time series and the errors have auto-correlation between themselves.As a result, the paper supposed to use EGARCH model to mine the tendency information of the above errors. Then we use the result to modify predicted value of the volatility of stocks. Finally, we study a case with the satisfactory result by the SPA test which is showing that this model is more accurate than other models.
引文
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