基于统计抽样的重尾协整检验

发布时间：2018-06-13 05:37

本文选题：重尾过程 + 协整检验　；参考：《山西大学》2016年硕士论文

【摘要】：协整是描述经济时间变量之间的一种均衡关系的理论,协整理论为处理复杂的宏观经济问题提供了有力的理论工具和数学模型.在长期的实证研究中,统计学家发现大部分的金融时间序列会呈现尖峰重尾的统计特征,于是重尾序列的研究成为统计学的研究热点.本文主要研究重尾过程的协整检验.由于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,而且用于协整检验统计量的渐近结果比较抽象,在实际应用过程中临界值的选取容易受重尾过程中奇异值的影响而不稳定,只具有理论意义.因此,在实际应用过程中还需要一些统计算法去逼近检验统计量的渐近分布.本文通过构造Subsampling抽样算法和Sieve Bootstrap抽样算法,在不估计重尾指数的情况下,分别基于Phillips-Perron(PP)方法与Augmented Dickey-Fuller(AD-F)方法,计算该检验统计量的临界值,并且证明Subsampling抽样算法和Sieve Bootstrap抽样算法在理论上的合理性.同时通过MonteCarlo模拟证明Subsam-pling抽样算法和Sieve Bootstrap抽样算法的有效性.最后运用本文的抽样算法对上海市税收收入和GDP之间的关系进行实证分析,说明该方法的实用性和有效性.
[Abstract]:Cointegration is a theory that describes the equilibrium relationship between economic time variables. The theory of cointegration provides a powerful theoretical tool and mathematical model for dealing with complex macroeconomic problems. In the long-term empirical research, statisticians found that most of the financial time series will show the statistical characteristics of peak and heavy tail, so the research of heavy-tailed series has become the research hotspot of statistics. This paper mainly studies the cointegration test of heavy tail process. Because the asymptotic distribution of cointegration test statistics for heavy-tailed processes contains an inestimable heavy-tailed exponent 伪, and the asymptotic results for cointegration test statistics are abstract, In practical application, the selection of critical value is vulnerable to the influence of singular value in heavy-tailed process, which is of theoretical significance. Therefore, some statistical algorithms are needed to approximate the asymptotic distribution of test statistics. In this paper, by constructing the subsampling sampling algorithm and the sieve bootstrap sampling algorithm, the critical values of the test statistic are calculated based on the Phillips-Perronn PPP method and the Augmented Dickey-Fuller AD-Fmethod, respectively, without estimating the heavy-tailed index. It is proved that the subsampling sampling algorithm and the sieve bootstrap sampling algorithm are reasonable in theory. At the same time, Monte Carlo simulation proves the validity of Subsam-pling sampling algorithm and sieve bootstrap sampling algorithm. Finally, the empirical analysis of the relationship between tax revenue and GDP in Shanghai is carried out by using the sampling algorithm in this paper, which shows the practicability and effectiveness of the method.
【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】：F224;F812.42;F127

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