One procedure might be to use the Johansen estimator to determine the cointegrating rank and then estimate the cointegrating vectors with the OLS method proposed pulling out the number of vectors determined by the Johansen test. Given the OLS estimates are fairly robust, one could then use the system errors to see if one has highly autocorrelated errors, correlated errors and or moving average errors. One can then move on to the Fully-Modified estimates, see if there is much change and try to explain the change, ensuring that it is not due to some spurious correlations at long lags caused probably be errors in the data.
The Johansen estimator is best only if the model is well specified without highly autocorrelated cointegrating errors. If one is unsure of the cointegrating dimensionality and is only trying to estimate one cointegrating vector, then the FM estimator is best. When one moves up to a multidimensional cointegrating space, the 'benchmark' multidimensional OLS proposed faired surprisingly well comparatively, so much so as to be clearly preferred immediately there were any problems (see Hargreaves, 1993).
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