As written in the title, I am looking for the stability condition of a vector error correction model (VECM).

I have found this phrase:

the companion matrix of a VECM with ๐พ endogenous variables and ๐‘Ÿ cointegrating equations has ๐พ โˆ’ ๐‘Ÿ unit eigenvalues. If the process is stable, the moduli of the remaining ๐‘Ÿ eigenvalues are strictly less than one.

Is this the correct condition? If so, could anyone tell me how we define "the companion matrix of a VECM"? Is it the coefficient matrix of X_(t-1) ?

In the end, how could I test this condition in R? Is there a package to do this?


I maybe have an answer which I'm not sure about : I think that I should transfer my VECM to a VAR form, and then I could analyse the Eigenvalues of the compagnon matrix of VAR. There should be r unit roots where r is the number of cointegration relationships, and the module of the rest Eigenvalue should be strictly inferior to 1.

The definition of a compagnon matrix could be found at page 7 and 8 of this link : http://economia.unipv.it/pagp/pagine_personali/erossi/rossi_VAR_PhD.pdf

Please confirm if my idea is correct. Also, if my question is not clear enough, please tell me.

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