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I need to include a stationary variable as an exogenous one in the Johansen cointegration test; however, I noticed that the following note appears when performing this test "critical values may be not valid with exogenous variables", so what critical values are valid in this case? Can you give me a reference please?

In this family of statistics the distributions are non-standard. Critical values are obtained by simulation of the statistic under various assumptions about the specification. For obvious reasons these simulations do not involve exogenous variables.

Therefore, when you estimate with exogenous variables, we report the simulation results, but with a warning that they might not be valid.

See the various references cited in the manual.

Thank You for the answer.
I've searched for articles related to my problem and in the Journal of Econometrics I've found an easy to implement solution.
The article calls "Approximations for cointegration tests with stationary exogenous regressors" (2005) from Boswijk and Doornik.

Probably Eviews don't know this solution. You only need to calculate the canonical correlation (see page 807 footnote 8 ). Instead of the results of a simulation Doornik and Boswijk use the Gamma distibution that provides an accurate approximation.

Please tell me if EViews is willing to approach the problem!

I'm not a cointegration expert and I hadn't seen that paper, but it sounds quite interesting. We haven't really looked at the Johansen tools in a few years, and haven't had requests to do so (which is one of the primary ways we decide what to do)...until now. We'll have someone take a look at it when we get the chance, but can't make any promises about if or when in might appear. Thanks for the suggestion and reference.