I have the below results based on the engle-granger test for cointegration, where the dependent and independent variables themselves are not stationary. The results show that null (process is not cointegrated) is rejected for lags 0,1,2 for both single mean and trend. However, lags 3,4,8 fail to reject the null. Is it then appropriate to run an AR(1,4) model, if we cannot reject the null that the process is cointegrated at lag 4?
Engle-Granger Cointegration Test