I have data with 4 variables that are rather trending upwards. They are mostly stationary at level, but only when I include a constant and trend into the ADF unit root test. They are not stationary without a constant or with a constant in the regression.
After differencing, all variables are stationary and thus I(1) (no constant, constant, constant and trend)
When conducting the Engle-Granger cointegration test with Gretl, should I include any constant, constant and trend into the test or rather go with "without constant"?
It seems when I choose "without constant" my results confirm the other Johansen Cointegration results while by including a constant or trend, my results conflict with criterion (a)
There is evidence for a cointegrating relationship if: (a) The unit-root hypothesis is not rejected for the individual variables, and (b) the unit-root hypothesis is rejected for the residuals (uhat) from the cointegrating regression.
If the results are lower 0.1 for the unit root tests, I can hardly confirm cointegration, as I find it with the Johansen Cointegration test, where I do include a constant and trend.