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), ...?

  • $\begingroup$ " 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? $\endgroup$
    – DanielOY
    Commented Sep 7, 2017 at 11:17
  • $\begingroup$ @RichardHardy I noticed this thread here but there was no follow-up on the user's question: stats.stackexchange.com/questions/60328/… $\endgroup$
    – DanielOY
    Commented Sep 7, 2017 at 18:39

1 Answer 1


as per my knowledge ARDL is applicable when some of your variables are I(O) and some are I(1), even you can use FOR ALL I(0) variables provided you don't have any spurious regression results. The idea of differencing time series is to make model stable.


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