The VEC model adjustment gives you the number of cointegration vectos that you specify in the VAR Specification/Cointegration setup window. And it has to be specified manually. So, if you specify 2 vectors, the VEC will be adjusted considering two coint. equations, independently of the cointegration result that you got previously (which it is supposed that you performed before right?).

The cointegration vector will consider all the variables that you specified in the VAR/Specification window. You can´t get a cointe eq with less vars once the cointegration equation is adjusted based on the VEC model that should consider the three variables used for the cointegration test.

See the p- value of the variables, the one which is less than 10% , 5% or 1% is taken as co integrated variable..

Goran,

If you run the Johansen cointegration test it normally gives you two statistics, the Maximum Eigen value and the Trace statistic. In both cases it will show you the number of hypothesized cointegrating equations for the three variables. First step is when the hypothesis of NO cointegration is Rejected as shown by the p-value of either the Trace or maximum Eigen value statistic at say 1%, 5% or 10%. The rejection of the Null Hypothesis (NO Cointegration) continues down the column with (i) At most 2; (ii) At most 3, etc, etc (number of hypothesized cointegrating equations) until you fail to reject the null at say At most 3 cointegrating vectors. Then you could say that there are at least three cointegrating relations between the variables. I may not have answered your question but I stand to be corrected (EVIEWS).

Barnabas Kiiza

Hi Goran,

We perform Johansen test to determine maximum possible cointegrating relationships when we have more than two variables. In case, we have only two variables in the first place, the Engle-Granger test will suffice. Since you have three variables to start with, Johansen test is more appropriate. However, there are two variants of Johansen cointegration tests; Trace and Maximum Eigenvalue tests. Sometimes, these tests indicate the same number of co-integrating relationships between I(1) variables and sometimes the test results differ identifying the number of cointegrating relationships. However, when the two test results vary, you should apply the Pantula principle, i.e. when one of the tests (either Trace or Max Eigenvalue) fails to reject the null hypothesis of no cointegration. That means you keep rejecting the null hypothesis of no cointegration until you can't do that anymore. Whichever version of the two tests fails to reject the null hypothesis the first, that will be the actual number of cointegration. Helmut Lutkephol's book has a lucid discussion on Trace and Maximum Eigenvalue tests (on the relative strength of the two test versions). You can go through that book if you want to. However, eventually, it depends what you want to do with the co-integrating relationships among the I(1) variables. If you want to forecast the variables, you need to proceed further by estimating the VECM equations after conducting the LR test (this test determines if the restrictions you may impose on the long run cointegrating relationships and the speed of adjustment variables are binding or not). In case you want to do the policy analysis, you need to conduct the impulse response analysis as well as variance decomposition test.

Thanks and good luck.

Hi All,

I want to ask, i am using Johansen cointegration technique and E-views Trace test indicates the existence of two cointegrating relationships. Could someone help in how to interpret the existence of two cointegrating relationships. Thanks