Is the Johansen test for cointegration linked to the rank-nullity theorem? In which way?
I believe that it is linked in some way, since the test contrasts if each eigenvalue is far enough from 0 to reject the null hypothesis (eigenvalue = 0), but I couldn't find it in any literature, and from the literature I have followed I thought that the multiplicity of 0 as an eigenvalue would give you the number of linear relationships (cointegration relationships) and in the Johansen Test it looks like we are doing the opposite: if the matrix rank rank is 0 and hence nullity = number of variables, we assume that there is no cointegration and hence no linear relationship amongst the variables included.