Is there a correct and up to date procedure? I just run the equation in VEC form and test the significance of the time trends? What are the possible problems that I should be aware of?
In the Johansen methodology there are five models
- unrestricted constant and unrestricted trend
- unrestricted constant and restricted trend
- unrestricted constant and no trend
- restricted constant and no trend
- no constant and no trend.
As these models are nested they can be tested sequentially using likelihood ratio tests.
For the usual sample sizes these processes can look very similar and the tests probably have low power and it is better to use your economic understanding of the variables involved. Chapter 5 of Johansen (1955), Likelihood -based inference in cointegrated vector autoregressive models contains more details of these models and their implication on the models being estimated.
In the residual based cointegration test the trend and constant can be included in the OLS estimation of the residuals and there is then no need to include a constant or trend in the cointegrating test regression. The decision to include a constant or trend in the first OLS estimation should be based on economic theory.