VAR process

Hi,

In every book on VAR [Vector auto regression] I see that, any VAR [p]
process can be expressed as a VAR [1] process. Here my question is how it
can be possible? When you change it to a VAR [1] process, the VCV matrix of
Innovations contains zero and hence it is not of full rank. Therefore it is
not a PD matrix, you cannot decompose that according cholesky decomposition
and lot more things can not be done with it because VCV matrix is singular.
Then how can that process be a VAR process?

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