# [R-SIG-Finance] [R-sig-finance] A question on VECM

John Frain frainj at tcd.ie
Thu Aug 20 11:56:48 CEST 2009

```The Example on page 303 of Lutkepohl is an examination of
cointegration properties of an interest rate R and inflation.  If
inflation were denoted by say pi then everything would be relatively
familiar,  However inflation is denoted by Dp.  Both R and Dp (pi) are
are I(1) leading to the estimated cointegrating relationships (7.2.30)
or (7.2.31).

In the original Engle and Granger (1987) Econometrica article all the
elements of the non-stationary vector were of the same order of
integration.  The treatment of stationary variables was not explicit
but  needed to be added afterwards.  the treatment in Lutkepohl
includes this explicitly into the vecm system.

Best Regards

John

2009/8/19  <markleeds at verizon.net>:
> John: now that I think of it, you're right in that , as far as I remember,
> both variables need to
> be I(1) for there to be a possible cointegration relation so I'll have to
> check out pg 303
> closer. It doesn't make sense for R_t to be stationary and still be part of
> a cointegrating
> relation ? So, my bad and I'll go back to 303 and see what's going on there.
> Thanks for the
> clarifiication but now I'm actually more confused and don'thave the energy
> to dig through Lutkepohl at the moment.
>
>
> Mark
>
>
>
> On Aug 19, 2009, John Frain <frainj at tcd.ie> wrote:
>
> Lutkepohl is splitting up the system into r stationary components or
> ecm's and n-r trends. He uses this ordering to show that that this
> can be done. The stationary components and the ecm's only enter the
> system at lag 1. The stationary components do not and should not
> enter the ecm's. If you do have stationary variables this is testable
> and may be imposed at estimation.
>
> Best Regards
>
> John
>
> 2009/8/19 RON70 <ron_michael70 at yahoo.com>:
>>
>> still no single reply. Should I need to design my query in better way?
>>
>>
>>
>> RON70 wrote:
>>>
>>> Hi all, in Lutkepohl, page 250, I found that if there are stationary
>>> variables in integrated system then they must be put in upper
>>> r-dimension.
>>> My quesltion is, is that the fact? If I do not do it, is there any
>>> problem
>>> in estimation and interpretation? I have done few exercises and found
>>> that
>>> parameter estimation is not infected with ordering (except IRF
>>> estimation). Even is page 303 an example is presented wherein inflation
>>> rate variable is taken as 2nd variable, although it looks like a stable
>>> process.
>>>
>>> Can anyone please clarify that? If really ordering is a problem in
>>> presence of a stationary variable, can anyone provide me an example, with
>>> perhaps in R-code so that I can regenerate?
>>>
>>> Thanks
>>>
>>
>> --
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>>
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>
>
>
> --
> John C Frain, Ph.D.
> Trinity College Dublin
> Dublin 2
> Ireland
> www.tcd.ie/Economics/staff/frainj/home.htm
> mailto:frainj at tcd.ie
> mailto:frainj at gmail.com
>
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--
John C Frain, Ph.D.
Trinity College Dublin
Dublin 2
Ireland
www.tcd.ie/Economics/staff/frainj/home.htm
mailto:frainj at tcd.ie
mailto:frainj at gmail.com

```