Good evening,

I have a probit model where:

probit(y) = intercept + beta1*var1 + beta2*var2 + beta3*var3 + beta4*var4

where after performing augmented dickey fuller through the - dfuller - command I obtain that:

y and var2 are both I(0)

var1, var3, var4 are I(1)

I read that since I have variables integrated of different orders, I should use an ARDL model (using command ardl) to test for Cointegration. However I'm not sure if I can because my dependent variable y is I(0). I have searched the web for some insight but I have found no conclusive answer. Is there a problem of using ARDL when y is binary? Is this a problem in probit/logit? Or would it only be a problem if I used LPM?

Additionally, sorry if the question is a bit basic but are all dummy variables I(0)?

Thank you