基于RJMCMC的Gamma分布尺度参数的多变点检测

发布时间：2018-08-11 20:39

【摘要】：变点问题作为统计学的一个重要研究方向,在金融、气象等领域中被广泛的作用。本文讨论了在独立的Gamma分布中尺度参数的多变点问题,利用可逆跳跃马尔可夫链蒙特卡罗算法(RJMCMC)去计算参数的后验分布以及变点的位置。基于该RJMCMC算法,对连涨连跌收益率进行了研究分析。在第一章中,简要概述了变点问题的由来,对变点问题在不同领域的应用研究进行了描述,并介绍了几种常见的研究方法,最后介绍了单变点问题和多变点问题的研究现状。第二章介绍了贝叶斯方法,列举了一些关于贝叶斯多变点问题的研究。描述了Gamma分布与Gamma分布族的概念,以及Gamma分布在现实中的应用。在第二章的最后给出了模型的假设,以及一些参数的先验分布。在第三章中,在贝叶斯估计、Monte Carlo方法、M-H算法的基础上提出了RJMCMC算法。给出了RJMCMC算法的步骤,计算出了Gamma分布的基于RJMCMC算法四个转换的接受概率。第四章设计了一个模拟例子来检验RJMCMC方法的正确性与高效性。首先生成有变点的Gamma分布序列,利用RJMCMC算法得出变点个数的估计,并与SN方法比较。第五章进行实证分析,运用RJMCMC算法对2000年到2015年的上证指数连涨连跌收益率进行变点检测分析,找出数据中存在的变点,根据所找出的变点位置,寻找变结构点附近政策的变化并加以分析第六章针对面板数据,采取基于最小二乘法的均值共同变点检验统计量,来探讨面板数据均值共同变点的存在性及估计,并对Nasdaq、Xetra DAX、Hangseng等六大股市的日收益率进行实证分析。第七章对本文进行了总结,同时给出不足以及展望。
[Abstract]:As an important research direction of statistics, change point problem is widely used in finance, meteorology and other fields. In this paper, we discuss the multivariate point problem of the scale parameter in the independent Gamma distribution, and use the reversible jump Markov chain Monte Carlo algorithm (RJMCMC) to calculate the posterior distribution of the parameter and the position of the change point. Based on the RJMCMC algorithm, the yield of continuous rise and fall is studied and analyzed. In the first chapter, the origin of the change point problem is briefly summarized, the application research of the change point problem in different fields is described, and several common research methods are introduced. Finally, the research status of the single change point problem and the variable point problem is introduced. In the second chapter, Bayesian method is introduced, and some researches on Bayesian variable point problem are listed. The concepts of Gamma distribution and Gamma distribution family and the application of Gamma distribution in reality are described. At the end of chapter 2, the hypothesis of the model and the prior distribution of some parameters are given. In chapter 3, the RJMCMC algorithm is proposed on the basis of Bayesian estimation Monte Carlo method and M-H algorithm. The steps of RJMCMC algorithm are given, and the acceptance probability of four transformations based on RJMCMC algorithm for Gamma distribution is calculated. In chapter 4, a simulation example is designed to verify the correctness and efficiency of RJMCMC method. First, the Gamma distribution sequence with variation points is generated, and the number of change points is estimated by using RJMCMC algorithm, and compared with SN method. The fifth chapter carries on the empirical analysis, uses the RJMCMC algorithm to carry on the change point detection analysis to the Shanghai stock market index from 2000 to 2015, finds out the change point which exists in the data, according to the location of the change point, Looking for the change of policy near the variable structure point and analyzing the sixth chapter, aiming at the panel data, taking the mean common change point test statistic based on the least square method to discuss the existence and estimation of the common change point of the panel data. The daily returns of six major stock markets, such as Nasdaq Xetra DAXG Hangseng, are analyzed empirically. The seventh chapter summarizes this paper, and gives the deficiency and prospect.
【学位授予单位】：合肥工业大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O212

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