I am fitting an error correction model (ECM) of two I(1) variables. I'm following the Engle-Granger approach of first finding the cointegrating relationship. So first, I regress one series against the other and then test for stationarity on the residuals.
I find that the ADF test does not reject the unit root hypothesis (not stationary) when no lags are included in the ADF test, but it does reject the unit root (stationary) when there are lags included. In other words, if I regress the change in residuals against the lag in the change in residuals and the lag of the residuals in levels, then I get strongly significant coefficients for the right-hand side variables. However, if only doing the regression of the change in residuals against the lag of the residuals in levels, then the slope is not sufficiently significant. I believe this is partially due to the fact that both of the original I(1) variables would best be fit by AR(2) models if only considered univariately.
I'm curious about the best way to proceed here. My sense is to just add lags of the change in the original I(1) variables to the ECM model. I shouldn't need to, for instance, include the change in the residuals (rather than just the lag) or something like that (it can cause problems with identification when including more lags to the ECM for other reasons).
