基于MCMC方法的上证股指波动性实证研究

发布时间：2018-07-01 18:06

本文选题：股指波动性 + GARCH模型　；参考：《江西财经大学》2012年硕士论文

【摘要】：目前,我国股票市场起步晚,尚属于新兴股票市场,与发达国家成熟的股票市场相比,在影响股市波动性方面存在着许多不同的地方,因而其所表现出来的特有性质对研究国内股票市场的波动性具有重要的意义。传统GARCH模型对参数估计的方法主要是基于极大似然理论的基础上,对模型进行最优化,但是由于GARCH模型对参数有一定的约束条件,故难以对模型的相关参数进行进一步的统计分析,同时在估计参数时往往存在偏离,难以达到实现最优化的目的。为了能更好地解决以上问题,本文尝试应用基于贝叶斯理论的马尔科夫蒙特卡罗(MCMC)方法来构建GARCH模型,以更好地描述上证股指收益率时间序列的波动性特征。本文从不同的角度系统地研究GARCH类模型的估计方法,以探索和研究贝叶斯统计的新领域,并针对性地对模型进行扩展。具体来说,本文运用MCMC方法对基于正态分布的GARCH(1,1)模型的参数进行估计,通过构造一个收敛于待估计参数的后验分布,从而绕开了GARCH模型中对参数的约束,解决了一般优化方法难以运用的困难。综合对比分析基于BHHH方法的GARCH模型和基于MCMC方法的GARCH模型在上证股指波动性的实证研究,试图更好地利用新模型来描述和解释股市的波动性特征,这对推动基于贝叶斯理论的MCMC方法在金融实践中的应用提供一定的参考价值。论文理论与实际相结合,既探讨了模型的理论研究,也进行了实证分析。在最后本文依据研究结果进行总结,并对今后的研究工作进行了展望。
[Abstract]:At present, the stock market of our country starts late and still belongs to the emerging stock market. Compared with the mature stock market in developed countries, there are many differences in influencing the volatility of stock market. Therefore, it is of great significance to study the volatility of domestic stock market. The traditional method of parameter estimation in GARCH model is based on the maximum likelihood theory to optimize the model, but the GARCH model has some constraints on the parameters. Therefore, it is difficult to make further statistical analysis on the related parameters of the model, and at the same time, there are often deviations in estimating the parameters, so it is difficult to achieve the goal of optimization. In order to solve the above problems better, this paper attempts to use the Markov Monte Carlo (MCMC) method based on Bayesian theory to construct the GARCH model to better describe the volatility characteristics of the time series of Shanghai stock index yield. In this paper, we systematically study the estimation methods of GARCH model from different angles, to explore and study the new field of Bayesian statistics, and extend the model. Specifically, this paper uses MCMC method to estimate the parameters of GARCH (1K1) model based on normal distribution. By constructing a posterior distribution which converges to the parameters to be estimated, the constraints of parameters in GARCH model are circumvented. The difficulty of general optimization method is solved. By comparing and analyzing the GARCH model based on BHHH method and the GARCH model based on MCMC method in Shanghai stock index volatility, this paper tries to use the new model to describe and explain the volatility characteristics of the stock market. It provides some reference value for the application of MCMC method based on Bayesian theory in financial practice. Combining theory with practice, this paper not only discusses the theoretical research of the model, but also makes an empirical analysis. Finally, according to the results of the research, the future research work is prospected.
【学位授予单位】：江西财经大学
【学位级别】：硕士
【学位授予年份】：2012
【分类号】：F224;F832.51

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