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

[John Frain]

I agree.  Reducing a VAR(p) to a VAR(1) in this way is simply a device
to generalise certain properties of a VAR(1) to a VAR(p) or possibly
to complete certain computations.  In a VAR(p) the covariance matrix
or the contemporaneous errors is in general non-diagonal.  The
Choleski decomposition was the original way of transforming the
contemporaneous variables so that the covariance of the disturbances
is diagonal and has nothing to do with the VAR(1) representation.   It
would be possible to work in terms of the VAR(1) representation but
this would be an unnecessary complication.  There are of course
various problems with this kind of analysis (e.g. uniqueness) and
structural VARs, relying on restrictions from economic theory are more
used today.

Best Regards

John

2009/1/27  <markleeds at verizon.net>:
> 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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>>
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-- 
John C Frain
Trinity College Dublin
Dublin 2
Ireland
www.tcd.ie/Economics/staff/frainj/home.htm
mailto:frainj at tcd.ie
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