Comparison And Application Of The Cointegration Rank Test

As for the problem of non-stationary time series in econometric model, the diagnosis and test for cointegration is the key point. The aim of cointegration rank test is to find whether a group of non-stationary series’linear combination has a stable equilibrium relationship. If it is, the established model has economic significance and won’t appear spurious regression problem. JJ cointegration theory proposed by Johansen is the mainstream method of cointegration rank test. Not only because of this test procedure is easy to understand, easy to be programmed, but also because the power of the test is very well and the cointegration test is relatively high and the size level is relatively small. Cheng (1993) found that when the sample length is short, Johansen’s likelihood ratio test often exists great bias. It is easy to make a wrong decision. What’s more, distribution of the residual series of models will also affect the JJ test statistics. Kleibergen and Paap (2006) used the singular value decomposition of a matrix to obtain a parameter that reflects rank reduction and got a rank statistic based on this parameter. In the non-stationary cointegration case, the limiting distribution of the new rank statistic is identical to that of the Johansen trace statistic.Basically, this paper firstly makes a comparison in theory of the two cointegration rank tests and the conclusion is that JJ cointegration trace test is more easily influenced by the residuals of the model, companied to SVD cointegration test. In Section3, the finite sample properties of the tests are explored through Monte Carlo methods and we assume the error term obeys Gauss distribution, Poisson distribution, Skewed-t distribution, the generalized error distribution (GED) and the mixed Poisson and Gauss distribution. We make a comparison between the two cointegration rank tests when the error term obeys in the five distribution forms. At the same time, we establish two basic econometric model-GARCH and Realized GARCH. Under the two models, we talk about the standard and Bootstrap size properties and sequential procedures for selecting the cointegration rank. We come to a conclusion that under the assumption of non-Gauss distribution, relatively to the JJ cointegration test method, the SVD cointegration rank test method have a advantage in both size distortions and power level, while under the assumption of the Gauss distribution, they have same result. And introducing Wild Bootstrap method in the two kinds of cointegration test processes, the power of the both test level are improved.In the last section of this paper, we establish a VAR model to study the dynamic relationship between china’s crude oil spot price and Dubai crude oil spot price who is the representative of Southeast Asia’s crude oil spot price. Both two cointegration rank test methods accept only one co-integrating vector.