I have few time series which are cointegrated. First I differenced the non-stationary series and fitted VAR after making them stationary. Later I fitted vector error correction model separately and obtained the long run and short run relationship. As I know taking difference removes the long run relationship of variables. So does that mean I can use VAR to explain the short run relationship even the series are cointegrated? If so can I compare the results of VAR model and short run results of VECM model?
Only the long-term relationship can be compared with the variables at levels of the VAR model and the VEC model when varaibles are cointegrated. But it is not correct to check the short-term relationship in the var model with the cointegrated variables.
The comparison between the two models may provide insights into how the variables respond to short-term shocks and how they adjust back to their long-run equilibrium relationships I think.
In the VAR with omitted ecm terms, your estimates will suffer from omitted variable bias. Some of the missing long-term adjustments will bias the effects of the short-run adjustment
If your VECM is disturbed it will return to a new equilibrium different from the initial equilibrium (assuming that the eigenvalues of the dynamic system are 1 or of modulus, less than one - or the characteristic roots of the system are 1 or of modulus, greater than 1).
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