As I understand, the VECM and Johansen test should be used when there could be multiple cointegration relation.The EG test works when only one co-integration relation exist.
In Engle-Granger 1987 paper, all examples are bivariate. In the "Econometric Analysis 7th Edition", only the Johansen method is apply to the example with multivariate series in the co-integration section 21.3.5. In the "Analysis of Integrated and Cointegrated Time Series with R", EG method is shown in bivariate example. The only example I found where EG test applied to multivariate case is in the paper "Stationary and cointegration tests:Comparison of Engle - Granger and Johansen methodologies".
Although the textbooks or papers doesn't explicitly says that EG should only be used on bivariate case and Johansen test should be used on multivariate case, I was wondering if this is a rule, and what the results would be if I do otherwise.
My questions are
Can I use the EG test on multivariate time series?
What is the consequence to use EG test when there is actually more than one co-integration vectors?
Do I still use the static regression in EG method to evaluate the long-run relationship?
A relevant post focuses on bivariate case
What's the practical difference between the Johansen vs Engle-Granger tests for cointegration?
Any comments would be appreciated.
