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I'm struggling with understand the difference between (and why there is this difference) the normalized cointegration vectors provided by the ca.jo function and the ones provided by cajorls and VECM (tsDyn package) functions.

Those are the results from ca.jo function, with the cointegration vectors normalized for the first variable LSELIC (the test returned r=2, LSELIC.l1 and LIBCBR.l1 are the two vectors of coefficients from that cointegrations relationships): enter image description here

The cajorls function "Returns a list object with elements of class lm for the restricted VECM and a matrix object with the normalized cointegrating vectors".

enter image description here

Ultimately, the VECM provides the same results of cajorls function: enter image description here

So, what is the "correct" normalization? Or, what I believe, what are the interpretations of these two normalized cointegration vectors for the same variable?

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  • $\begingroup$ Is the difference not that one is restricted and the other is unrestricted? That would seem to be an obvious answer. $\endgroup$ Commented Jun 11 at 7:13
  • $\begingroup$ Right. I dind't understand the meaning of "restricted" in cajorls and VECM functions, since ca.jo function already provided a normalized vector for the first variable (LSELIC). Could you explain it? $\endgroup$ Commented Jun 12 at 3:24
  • $\begingroup$ I do not remember what that means (if I ever knew). If you cannot find the answer in the help file of cajorls, consider contacting the author of the R package. $\endgroup$ Commented Jun 12 at 6:53

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