重尾过程的协整检验

发布时间：2018-05-30 03:39

本文选题：重尾过程 + 协整过程　；参考：《山西大学》2016年硕士论文

【摘要】：协整过程是一种特殊的向量单位根过程,协整关系反应变量之间存在着长期稳定的均衡关系,在实际经济问题中,金融经济数据往往具有尖峰重尾的统计特点,难以用高斯分布去拟合,于是近年来重尾序列成为统计学及相关领域的一个研究热点。重尾过程协整检验统计量的渐近分布中含有不可估计的重尾指数α,本文针对这个问题,在不估计重尾指数α的情况下,运用bootstrap抽样和block bootstrap抽样两种算法,得出检验重尾过程协整关系的临界值,证明在两种抽样算法下检验统计量的收敛性,并进行实验模拟说明这两种抽样算法的有效性。本文共分为六章:第一章,前言,简要介绍了协整过程及重尾过程的研究背景。第二章,预备知识,主要介绍了协整过程和重尾分布及其相关知识。第三章,介绍了重尾协整过程的bootstrap抽样算法,证明了该算法的合理性并进行Monte Carlo模拟说明该方法的有效性。第四章,介绍重尾协整过程的block bootstrap抽样算法,进行证明说明该算法的合理性,最后运用Monte Carlo模拟说明该方法的有效性,第五章,进行实证分析,运用两种抽样算法对我国股票指数与经济增长进行协整关系的检验。第六章,总结与展望,总结本文主要内容,提出本文中两种算法的不足之处,以及日后需要改进的地方。
[Abstract]:The cointegration process is a special vector unit root process. There is a long-term stable equilibrium relationship between the cointegration response variables. In the actual economic problems, the financial economic data often have the statistical characteristics of sharp peak and heavy tail. It is difficult to fit with Gao Si distribution, so heavy-tailed sequence has become a hotspot in statistics and related fields in recent years. The asymptotic distribution of cointegration test statistics for heavy-tailed processes contains an inestimable heavy-tailed exponent 伪. In this paper, two algorithms, bootstrap sampling and block bootstrap sampling, are used to solve this problem without estimating the heavy-tailed exponent 伪. The critical value of cointegration relation of heavy-tailed process is obtained, and the convergence of the test statistics is proved under two sampling algorithms, and the validity of the two sampling algorithms is illustrated by experimental simulation. This paper is divided into six chapters: the first chapter, preface, briefly introduces the cointegration process and heavy-tailed process research background. The second chapter, preparatory knowledge, mainly introduces the cointegration process, heavy-tailed distribution and related knowledge. In chapter 3, the bootstrap sampling algorithm for heavy-tailed cointegration process is introduced, the rationality of the algorithm is proved and the validity of the method is illustrated by Monte Carlo simulation. In chapter 4, the block bootstrap sampling algorithm of heavy-tailed cointegration process is introduced, and the rationality of the algorithm is proved. Finally, the validity of the method is illustrated by Monte Carlo simulation. In chapter 5, the empirical analysis is carried out. Two sampling algorithms are used to test the cointegration relationship between stock index and economic growth in China. The sixth chapter summarizes and prospects the main contents of this paper and puts forward the shortcomings of the two algorithms in this paper as well as the future needs to be improved.
【学位授予单位】：山西大学
【学位级别】：硕士
【学位授予年份】：2016
【分类号】：O212;F224

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