Pesaran ARDL Model for testing cointegration relationship - How many variables?

I have a question related to a recent thread on CrossValidated.

Pesaran et al. (2001) propose an ARDL model that tests for cointegration with a bounds testing approach. What didn't get clear to me, after reading a few discussions and the paper, is following:

Can the ARDL model be applied to a bivariate system, or does it need more than two variables?

Or: Does the model work when testing X:I(0),Y:I(1) only? Or does it only work for multivariate systems, such as X:I(0), Y:I(1), Z:I(1), W:I(0), ...?

• " The asymptotic distributions of these statistics are non-standard under the null hypothesis that there exists no level relationship, irrespective of whether the regressors are I0 or I1. Two sets of asymptotic critical values are provided: one when all regressors are purely I1 and the other if they are all purely I0. These two sets of critical values provide a band covering all possible classifications of the regressors into purely I0, purely I1 or mutually cointegrated." If if read this correctly, then we could even test two I(0) variables? – DanielOY Sep 7 '17 at 11:17
• @RichardHardy I noticed this thread here but there was no follow-up on the user's question: stats.stackexchange.com/questions/60328/… – DanielOY Sep 7 '17 at 18:39