I have some data which had to be logged and differenced once to induce stationary. I ran the Johansen test for cointegration and found that it is present in my data set.

Does this fact tell me that using a VECM is more appropriate than using a VAR, despite of data now no longer being I(1)?


If your original or logarithmically-transformed variables are I(1) and cointegrated, then VECM is the correct model. Unrestricted VAR in levels is misspecified due to missing restrictions because of cointegration, while VAR for variables in first differences is misspecified because it omits the error correction terms (ECTs).

Now whether VECM is preferred over VAR for a particular objective is not clear cut. For example, if the ECTs are estimated with high variance, their inclusion may result in worse forecasting performance than that of VAR in first differences (in which the ECTs are omitted). This is a special case of the more general fact that correctly specified models with estimated (rather than known) parameters need not be the best models for forecasting, which is because of estimation imprecision.

  • $\begingroup$ Is it possible to have a VECM if I(0) and variables are co integrated? $\endgroup$ – EconJohn Nov 2 '17 at 19:31
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    $\begingroup$ @EconJohn, Variables cannot be cointegrated if they are I(0) to begin with. There have been a few threads addressing this if you want to get more references. $\endgroup$ – Richard Hardy Nov 2 '17 at 19:43
  • $\begingroup$ Ah, can you post the threads? $\endgroup$ – EconJohn Nov 2 '17 at 20:02
  • $\begingroup$ @EconJohn, check out some from this list. $\endgroup$ – Richard Hardy Nov 2 '17 at 20:09

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