I'm trying to understand what is the meaning of having a k x k parameter matrix for the long term (cointegration) relationship in a VECM model, and a rank r such that 0 < r <= k.

The way I understand it for now (and I'm not sure if this is correct) is that if r = k then there are k cointegrated relationships in the system, meaning that all the time series are at least cointegrated with another time series. If r < k then there are k - r time series that are not cointegrated with any other time series in the system and hence those ones can be represented by a simple VAR model, is this correct?



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