Hi;
 
Before I put a Gretl's example. Data set which I study is monthly. I have 101 observations and, if I apply the Johansen's tests in it, I obtain following output:
 

 

Rank

Eigenvalue

Trace

 p-value

L-máx

 p-value

 

0

0,11637

13,736

[0,3151]

11,01

[0,2600]

1

0,030163

2,7258

[0,6392]

2,7258

[0,6380]

 
Then I question to my self: if two hypothesis are accepted, why we must conclude that there aren't any cointegration relationships??? To conclude that I think we have to interpretate sequently, that is, starting with the less rank, the first rank we accept it will be the rank of cointegration, won´t it? In this case rank zero, doesn´t it? 
 
If the null hypothesis in L-max were that there are exactly "r0" ( and no r<=r0 as the trace test)) cointegration vectors, it would impossible the interpretation, because the rank would be, at the same time, zero and one. In a lot of articles there is that distintion between both tests.
 
I continue thinking that this isn't very clear in Gretl
 
Cheerssssss and thanksss
Javi