基于马尔科夫转换ARCH模型的上证综指波动率研究

发布时间：2019-03-27 06:46

【摘要】：作为经济走势的晴雨表，我国的股票市场在经过了20多年的发展，积累了较大的泡沫成分，体现出一定程度的市场波动性，故度量、刻画分析波动的特征有着重要的意义。本文以上证综指收益率序列为例，对于这类复杂的金融数据，采用极大似然估计方法得出简单的GARCH族模型无法刻画出波动序列的尖峰厚尾性，聚集性，长期记忆性以及杠杆性等诸多特征。因此，为了能够更好的刻画出波动特征，本文首先尝试利用R/S分析法，，假设残差分别在正态分布、t分布、GED分布及SKT分布下，使用“滚动时间窗”的方法对波动率进行预测，并采用ARFIMA(p,d,q)-EGARCH(m,n)-M模型对收益率序列进行了实证分析。实证结果表明：上证收益率序列存在长记忆性；基于SKT分布条件下ARFIMA(2,1)-EGARCH(1,1)-M模型能够较好的处理序列尖峰厚尾和聚集等特征并且较其他分布条件下具备较强的预测精度。随后在GARCH族模型的基础上，结合了马尔科夫机制转换的状态空间模型对其进行了扩展，文中讨论了三状态的MS-ARCH(3)模型，并且采用MCMC方法对参数进行估计，将采样Metropolis-Hasting取样法嵌套于Gibbs取样法中的方法，对参数进行取样。研究发现：MS-ARCH模型比GARCH族模型在刻画波动聚集特征方面表现的更优异，尤其是能够处理GARCH族所不能刻画的结构突变的特点，MS-ARCH优势还体现实际应用方面，如危机预警的作用。此外，还建议投资者把握好高波动时的获益机会，但是当高波动状态开始大量聚集的时候，就要提高警惕，谨防危机带来的损失。
[Abstract]:As a barometer of economic trend, after more than 20 years of development, China's stock market has accumulated a large bubble component, reflecting a certain degree of market volatility, so it is of great significance to measure and depict and analyze the characteristics of volatility. This paper takes the return series of Shanghai Composite Index as an example. For this kind of complex financial data, using the maximum likelihood estimation method, the simple GARCH family model can not depict the peak-thick-tail property and aggregation of the volatility series, and the method of maximum likelihood estimation is used to obtain a simple GARCH family model. Long-term memory and leverage and many other characteristics. Therefore, in order to better characterize the wave characteristics, this paper first attempts to use the RES analysis to assume that the residuals are under the normal distribution, t distribution, GED distribution and SKT distribution, respectively, and that the residual error is in the normal distribution, t distribution, SKT distribution and so on. ARFIMA (p, d, Q)-EGARCH (m, n)-M model is used to predict the volatility using the "rolling time window" method, and the empirical analysis of the yield series is carried out. The empirical results show that there is a long memory in the return series of Shanghai Stock Exchange. Based on the SKT distribution, the ARFIMA (2,1)-EGARCH (1,1)-M model can better deal with the characteristics of peak, thick tail and aggregation of the sequence, and has better prediction accuracy than other distribution conditions. Then on the basis of GARCH family model, it is extended by the state space model of Markov mechanism transformation. The three-state MS-ARCH (3) model is discussed in this paper, and the MCMC method is used to estimate the parameters. The sampling Metropolis-Hasting sampling method is nested in the Gibbs sampling method, and the parameters are sampled. It is found that the MS-ARCH model performs better than the GARCH model in describing the characteristics of wave aggregation, especially in dealing with the characteristics of structural changes that can not be characterized by the GARCH family. The advantages of MS-ARCH are also reflected in the practical application, and the advantages of GARCH model are better than those of the GARCH family. Such as the role of crisis warning. In addition, investors are advised to take advantage of high volatility, but when high volatility begins to gather in large numbers, be vigilant and beware of the losses caused by the crisis.
【学位授予单位】：华东交通大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：F224;F832.51

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