Quick question because I see this presented in different ways. Suppose the output from the @JOHMLE procedure is:
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Unrestricted eigenvalues and -T log(1-lambda)
Rank EigVal Lambda-max Trace Trace-95% LogL
0 1198.3102
1 0.1068 16.4915 17.7699 15.4100 1206.5560
2 0.0087 1.2784 1.2784 3.8400 1207.1952
I assume that "Rank 1" means a test of the null that the rank is 0 versus the alternative that the rank is at least 1 and "Rank 2" is the null that the rank is less than or equal to one against the alternative that the rank is 2. So then "Rank" here is essentially the alternative hypothesis, so that in this case there is one cointegrating vector.