[R-SIG-Finance] [R-sig-finance] VAR process

markleeds at verizon.net markleeds at verizon.net
Tue Jan 27 06:38:06 CET 2009

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 
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?
> -- 
> View this message in context: 
> http://www.nabble.com/VAR-process-tp21530701p21678648.html
> Sent from the Rmetrics mailing list archive at Nabble.com.
> _______________________________________________
> R-SIG-Finance at stat.math.ethz.ch mailing list
> https://stat.ethz.ch/mailman/listinfo/r-sig-finance
> -- Subscriber-posting only.
> -- If you want to post, subscribe first.

More information about the R-SIG-Finance mailing list