Good day all,

I have a question about three cointegration tests: the Engle-Granger (E-G), Johansen, and the Gregory-Hansen.

context: Most studies i ready rely on the Gregory-Hansen as a test of last resort - where the other two have failed to find cointegration. I understand why, the E-G and Johansen do not consider breaks in the cointegrating relationship. Thus, their failure to find a cointegrating relationship might be due to the presence of breaks in the cointegrating relationship. Using the Gregory-Hansen in this case will reaffirm the absence of cointegration, or suggest the other tests fail to find cointegration due to failure to account for breaks.

My question: how do we interpret results where either the E-G or the Johansen find cointegration, but the Gregory-Hansen does not? do we simply see it as "there is no cointegration in the presence of breaks" - meaning the E-G and Johansen results are still valid i.e. there is indeed cointegration, it just does not have breaks.

(the ADF, PP and Zivot andrews unit root tests all suggest variables are I(1)

Your assistance would be highly appreciated