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

[John Frain]

Let beta be (r by n) of rank r. (r<n).  Let Q (r by r) be the first r
columns of this matrix. Let P = inv(Q).  Then P * pi is of the form
you require.  (I presume that Q is always invertible - see
Johansen(1995), Likelihood based inference in Cointegrated Vector
Autoregressive Models, Oxford.).  In the early days this method was
seen as one way of achieving identification of the model. Regrettably,
in most cases, it does not have any economic content

Best regards

John

2009/6/4 RON70 <ron_michael70 at yahoo.com>:
>
> Right now I am not interested on estimation however trying to convince myself
> to justify this statement "normalization is always possible if variables
> arranged properly". I am trying to answer "why and how it is always
> possible?"
>
> PS: we know that having information on C.I. matrix does not improve coef
> estimation as rate of convergence for C.I. coef are much faster than rest.
>
>
>
> Pfaff, Bernhard Dr. wrote:
>>
>> Dear Ron,
>>
>> if I understand you correctly, you have a-priori knowledge about some of
>> the CI-relations? If so, why don't you compute them in advance and then
>> work further? This would also reduce the dimension of your VECM.
>>
>> Best,
>> Bernhard
>>
>> ps: Incidentally, the returned list element 'beta' of cajorls is computed
>> pretty much in sync what you have quoted, i.e., "normalization is always
>> possible if variables arranged properly".
>>
>>
>>
>>>Von: r-sig-finance-bounces at stat.math.ethz.ch
>>>[mailto:r-sig-finance-bounces at stat.math.ethz.ch] Im Auftrag von RON70
>>>Gesendet: Donnerstag, 4. Juni 2009 11:30
>>>An: r-sig-finance at stat.math.ethz.ch
>>>Betreff: Re: [R-SIG-Finance] [R-sig-finance] A question on VECM
>>>
>>>
>>>Thanks Bernhard for this reply.
>>>
>>>However actually I was thinking there might be some matrix
>>>property for any
>>>rxn (rank "r") matrix to equivalently explain in a combination
>>>of Identity
>>>and rx(n-r) matrices. Is it so? Actually I got this feeling
>>>from a statement
>>>saying that, "normalization is always possible if variables arranged
>>>properly". Therefore suppose I have some economic theory to
>>>express C.I.
>>>vectors in original term i.e. arbitrary C.I. matrix, based on some
>>>economics. Then I arrange them i.e. do matrix manipulation to make C.I.
>>>matrix Normalized i.e. let say, I have following original C.I.
>>>matrix (based
>>>on some economics) on 10 variables :
>>>
>>>n = 10
>>>r = 4
>>>C.I.matrix = matrix(rnorm(10*4), 4)
>>>
>>>Now I want to make it (I[4], C.I.matrix.modified[4x6] )
>>>
>>>Here I am rather interested is there any R function to do this kind of
>>>"matrix-normalization", not so interested to get a "already
>>>normalized" C.I.
>>>matrix.
>>>
>>>Is there any?
>>>
>>>Thanks
>>>
>>>
>>>
>>>Pfaff, Bernhard Dr. wrote:
>>>>
>>>>>-----Ursprüngliche Nachricht-----
>>>>>Von: r-sig-finance-bounces at stat.math.ethz.ch
>>>>>[mailto:r-sig-finance-bounces at stat.math.ethz.ch] Im Auftrag von RON70
>>>>>Gesendet: Mittwoch, 3. Juni 2009 10:19
>>>>>An: r-sig-finance at stat.math.ethz.ch
>>>>>Betreff: [R-SIG-Finance] [R-sig-finance] A question on VECM
>>>>>
>>>>>
>>>>>In my textbook, I found that for a vector error correction
>>>>>model, the "beta"
>>>>>matrix i.e. which represents the co-integrating vectors can be
>>>>>represented
>>>>>in a speacial matrix wherein first rxr partition is Identity
>>>>>matrix like :
>>>>>
>>>>>beta[rxn] = (I(r), beta[rx(n-r)])
>>>>>
>>>>>Is there any R function to do that representation?
>>>>>
>>>>
>>>> Dear Ron?
>>>>
>>>> have you considered the CRAN package 'urca' and there the function
>>>> cajorls()?
>>>>
>>>> library(urca)
>>>> example(cajorls)
>>>>
>>>> Best,
>>>> Bernhard
>>>>
>>>>
>>>>>Regards,
>>>>>--
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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