协整秩检验的比较研究及其应用

发布时间：2018-09-15 18:57

【摘要】：在利用计量模型进行分析时,由于数据可能是非平稳的序列,对多个序列间的协整关系进行诊断检验非常关键。对一组非平稳序列进行协整检验就是为了决定序列的线性组合是否存在长期稳定的均衡关系。只有存在稳定的均衡关系时,利用非平稳序列建立计量模型才有实际经济意义,才不会出现“伪回归”问题。Johansen和Juselius(1990)共同提出的似然比检验(本文使用JJ协整检验)是当前检验非平稳序列协整关系的主流方法,不仅仅是因为这一检验方法易于理解,便于编程,更是因为该方法的功效水平比较高而扭曲水平相对较小的缘故。然而,随着研究的深入,Cheng等(1993)发现,在样本长度较小时,JJ协整检验常常会存在很大的偏差,以至于过多的接受存在协整关系的假设,从而造成误判；另外,JJ检验统计量对扰动项的分布形式是敏感的。Kleibergen和Paap (2006)在研究矩阵的秩检验过程中引入了奇异值分解(SVD)方法,得到一个基于SVD的秩检验统计量,同时,他还证明这个秩检验统计量的渐近分布形式与Johansen协整迹检验相似。SVD秩检验方法与JJ协整迹检验相比,有哪些优缺点,文献中并未做过多的说明。基于此,本文首先从JJ协整检验和SVD的协整秩检验的理论方面进行比较研究,得到的结论是：JJ协整检验的检验统计量是基于序列的回归扰动项矩阵的,所以相对于直接对协整矩阵进行秩化简的SVD协整检验来说,JJ协整检验更容易受到扰动项序列分布形式的影响。在本文的模拟研究部分,首先利用有限样本进行数据模拟实验,对数据生成过程中的随机扰动项分别设定为服从标准高斯分布、泊松分布、Skewed-t分布、广义差分误差分布(GED)和混合泊松—高斯分布五种形式,然后分别利用这两种协整检验方法进行分析比较；其次,本文结合实际模型中的随机扰动项的分布可能存在“尖峰”,“厚尾”和“有偏”的特征,分别在上述五种形式的分布假定下建立GARCH模型和Realized GARCH模型并生成非平稳序列,然后利用JJ迹检验和SVD的秩检验方法研究协整检验的扭曲水平和功效水平,得到如下结论：在非高斯分布的假定下,SVD秩检验方法相对于JJ协整迹检验方法的检验扭曲水平较小,检验功效水平较大而在高斯分布的假定下两者表现差不多。在这两种协整检验过程中引入Wild Bootstrap方法,其检验的功效水平均得到明显的提高,这两种协整秩检验方法在检验效果上是差不多的。本文最后利用中国原油价格水平和迪拜原油(东南亚原油的代表)价格水平建立VAR模型,利用上述两种协整检验方法进行分析,结果表明均接受存在一个协整关系的假设检验。
[Abstract]:When using the econometric model to analyze, because the data may be a non-stationary sequence, it is very important to diagnose and test the cointegration relationship between multiple sequences. The cointegration test of a group of nonstationary sequences is to determine whether the linear combination of the sequence has a stable equilibrium relationship for a long time. Only when there is a stable equilibrium relationship, it is of practical economic significance to establish econometric models by using non-stationary sequences. The likelihood ratio test proposed by Johansen and Juselius (1990) (this paper uses JJ cointegration test) is the main method to test non-stationary sequence cointegration, not only because it is easy to understand. Easy to program, but also because the effectiveness of the method is higher and the distortion level is relatively small. However, with the further study of Cheng et al. (1993), it is found that the JJ cointegration test often has a large deviation when the sample length is small, so that too much acceptance of the hypothesis of cointegration relationship exists, resulting in misjudgment. In addition, JJ test statistics are sensitive to the distribution form of perturbation terms. Kleibergen and Paap (2006) introduced a singular value decomposition (SVD) method in the rank test of the study matrix, and obtained a rank test statistic based on SVD. At the same time, He also proves that the asymptotic distribution of the rank test statistic is similar to that of the Johansen cointegration test. The advantages and disadvantages of the rank test method compared with the JJ cointegration test are not explained too much in the literature. Based on this, this paper makes a comparative study on the theory of JJ cointegration test and SVD's cointegration rank test. The conclusion is that the test statistics of the WJJ cointegration test are based on the regression perturbation term matrix of the sequence. Therefore, compared with the SVD cointegration test which directly simplifies the rank of the cointegration matrix, the JJ cointegration test is more easily affected by the distribution form of the perturbed term sequence. In the part of the simulation research of this paper, first of all, we use finite samples to carry out data simulation experiments, and set the random disturbance terms in the process of data generation as standard Gao Si distribution, Poisson distribution and Skewed-t distribution, respectively. The generalized difference error distribution (GED) and Poisson Gaussian mixture distribution are analyzed and compared respectively by using these two cointegration test methods. Secondly, the distribution of random disturbance terms in the actual model may have "spikes". For the characteristics of "thick tail" and "biased", the GARCH model and the Realized GARCH model are established under the above five forms of distribution assumptions, respectively, and the non-stationary sequences are generated. Then the distortion level and efficacy level of cointegration test are studied by using JJ trace test and SVD rank test method. The following conclusions are obtained: under the assumption of non-Gao Si distribution, the distortion level of SVD rank test method is smaller than that of JJ cointegration test method. Test efficacy level is larger and in Gao Si distribution under the assumption that the two performance is similar. When the Wild Bootstrap method is introduced into the two cointegration tests, the efficiency level of the two cointegration test methods is obviously improved, and the two cointegration rank test methods have the same effect. In the end, the VAR model is established by using the price level of Chinese crude oil and Dubai crude oil (the representative of Southeast Asian crude oil), and the above two cointegration test methods are used to analyze the model. The results show that both of them accept a hypothesis test of cointegration relationship.
【学位授予单位】：浙江工商大学
【学位级别】：硕士
【学位授予年份】：2013
【分类号】：F224;F426.22

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