VAR process
I didn't respond earlier because I'm not clear on what the problem is
with rewriting it as VAR(1) ? Lutkepohl text shows how this is done on
pages 15 an 16 of his text. Except for the first row, the rest of the A
matrix is composed of identity matrices. They y_t* below the first
element play no role essentially because they are already known because
they are in {t-1,t-2,t-3.... }. The only noise
term is the first element, u_t associated with the first element y_t.
I agree that ithe Cov is not of full rank when you write it that way but
I don't know of any negative repurcussions of that. I think it's more of
a tool that he uses to show what the stability condition reduces to for
a VAR(p) and nothing more than that. This same type of technique is used
when
writing AR models in state space form.
Hopefully Eric or Bernhard or someone else can say more but I think it's
just used for
deriving the stability condition in a easier way.
On Mon, Jan 26, 2009 at 9:42 PM, RON70 wrote:
Hi, More than one week, still no suggestion. Is my question not understandable or answerable? Regards, RON70 wrote:
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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