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-max    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