Johansen Cointegration test

[Manj91]

Hi guys,

I have a question on the Johansen co-integration test. If I am correct there are 5 posible models with different degrees of freedom.
I have read the best models are 2,3 and4.
Do all of the models need to have co-integrating vecors for there to be cointegration?
For my data model 2 and 4 have co-integrating vectors but model 3 doesnt. So would I say there was co-integration or not?
very confusing.
any help is appreciated.
Thanks!