[Sebastian Kripfganz]

With small samples, you should use the finite-sample critical values provided in Kripfganz and Schneider (2020, Oxford Bulletin of Economics and Statistics), which are available from the ardl postestimation command estat ectest. If the sample is really small, the command may not report such critical values because they are too unreliable. You could still use asymptotic critical values from PSS or resort to the bootstrap, but they won't be more reliable.

[ahmed mohamed ak]

Why is it necessary for the variables to have the same order of integration to apply the ARDL approach, when the original paper indicates that it is applicable regardless of whether the variables are are purely I(0), purely I(1), or mutually cointegrated?

[Sebastian Kripfganz]

It is not necessary for the vaiables to have the same order of integration.

[ahmed mohamed ak]

We would appreciate it if you could explain Hypothesis 5b to us, Professor.