重尾序列持久性变点检验的统计分析
发布时间：2018-08-27 15:03
【摘要】：对于变点问题的研究最早是被应用到工业质量控制领域当中,目前它不仅是在工业质量控制领域里有大量的应用,在经济,金融,医学,计算机,网络安全,信号跟踪等领域里也有很重要的应用.近些年来,由于持久性变点问题在实际生活中有重要的应用,因此对它的研究得到了经济学家的广泛关注.但是许多与金融有关的数据都具有尖峰厚尾的特点,因此对重尾序列持久性变点的研究显得尤为重要.本文给出了两种重尾持久性变点的检验方法.第一种是在原假设为I(1),备择假设为I(0)-I(1)下利用比率统计量来检验变点,第二种方法是在原假设为I(0),备择假设为I(0)-I(1)下利用Wild bootstrap抽样方法来对变点进行检验.通过数值模拟得到了各自的经验水平值和经验势函数值,发现这两种方法对解决该问题都是有效的.论文主要由五部分组成.第一章是引言.本章主要对变点问题进行了描述,并简单介绍了已有的一些变点检验的方法:极大似然法,最小二乘法,累积和法,经验分位数法.第二章是理论基础知识.本章主要介绍了与本文有关的一些背景知识.第三章是重尾持久性变点的比率检验.本章主要研究了原假设是I(l),备择假设为I(0)-I(1)的残差比率检验,并给出了它在原假设下的渐近分布和备择假设下的收敛速度.通过数值模拟得到了此方法下的经验水平值和经验势函数值.第四章是基于Wild bootstrap的重尾持久性变点检验.本章主要主要研究了原假设为I(0),备择假设为I(0)-I(1)的残差比率检验,并给出了它在原假设下的渐近分布.然后利用Wild bootstrap算法对其进行抽样,发现它们的渐近分布是一致的,通过数值模拟.得到了此方法下的经验势函数值.第五章是总结.这一章对本文的主要内容进行了总结.
[Abstract]:The study of the change point problem was first applied to the field of industrial quality control. At present, it not only has a large number of applications in the field of industrial quality control, but also in economics, finance, medicine, computer, network security. There are also important applications in areas such as signal tracking. In recent years, due to the important application of persistent change point problem in real life, its research has been widely concerned by economists. However, many data related to finance have the characteristics of peak and thick tail, so it is very important to study the persistent change point of heavy-tailed sequence. In this paper, two testing methods for persistent change points with heavy tail are given. The first method is to test the change point by using ratio statistics under the original hypothesis I (1) and the alternative assumption I (0) -I (1). The second method is to test the change point by using Wild bootstrap sampling method under the original assumption of I (0) and the alternative assumption of I (0) -I (1). The numerical simulation results show that both the empirical level and the empirical potential function are effective to solve the problem. The paper consists of five parts. The first chapter is the introduction. In this chapter, we mainly describe the problem of change points, and briefly introduce some existing methods of change point test: maximum likelihood method, least square method, cumulative sum method and empirical quantile method. The second chapter is the basic knowledge of theory. This chapter mainly introduces some background knowledge related to this paper. The third chapter is the ratio test of heavy-tailed persistent change points. In this chapter, we mainly study the residual ratio test of the I (l), alternative hypothesis I (0) -I (1), and give its asymptotic distribution under the original hypothesis and the convergence rate under the alternative hypothesis. The empirical level value and empirical potential function value are obtained by numerical simulation. Chapter 4 is the heavy-tailed persistence change point test based on Wild bootstrap. In this chapter, we study the residual ratio test of I (0) and I (0) I (1), and give its asymptotic distribution under the original hypothesis. Then the Wild bootstrap algorithm is used to sample them and it is found that their asymptotic distributions are consistent. The value of empirical potential function in this method is obtained. The fifth chapter is a summary. This chapter summarizes the main contents of this paper.
【学位授予单位】：山西大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O212.1;F840
本文编号：2207639
[Abstract]:The study of the change point problem was first applied to the field of industrial quality control. At present, it not only has a large number of applications in the field of industrial quality control, but also in economics, finance, medicine, computer, network security. There are also important applications in areas such as signal tracking. In recent years, due to the important application of persistent change point problem in real life, its research has been widely concerned by economists. However, many data related to finance have the characteristics of peak and thick tail, so it is very important to study the persistent change point of heavy-tailed sequence. In this paper, two testing methods for persistent change points with heavy tail are given. The first method is to test the change point by using ratio statistics under the original hypothesis I (1) and the alternative assumption I (0) -I (1). The second method is to test the change point by using Wild bootstrap sampling method under the original assumption of I (0) and the alternative assumption of I (0) -I (1). The numerical simulation results show that both the empirical level and the empirical potential function are effective to solve the problem. The paper consists of five parts. The first chapter is the introduction. In this chapter, we mainly describe the problem of change points, and briefly introduce some existing methods of change point test: maximum likelihood method, least square method, cumulative sum method and empirical quantile method. The second chapter is the basic knowledge of theory. This chapter mainly introduces some background knowledge related to this paper. The third chapter is the ratio test of heavy-tailed persistent change points. In this chapter, we mainly study the residual ratio test of the I (l), alternative hypothesis I (0) -I (1), and give its asymptotic distribution under the original hypothesis and the convergence rate under the alternative hypothesis. The empirical level value and empirical potential function value are obtained by numerical simulation. Chapter 4 is the heavy-tailed persistence change point test based on Wild bootstrap. In this chapter, we study the residual ratio test of I (0) and I (0) I (1), and give its asymptotic distribution under the original hypothesis. Then the Wild bootstrap algorithm is used to sample them and it is found that their asymptotic distributions are consistent. The value of empirical potential function in this method is obtained. The fifth chapter is a summary. This chapter summarizes the main contents of this paper.
【学位授予单位】：山西大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O212.1;F840
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相关期刊论文 前2条
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2 秦瑞兵;田铮;金浩;;持久性变点的非参数检验[J];西北工业大学学报;2010年02期
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