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

RON70 ron_michael70 at yahoo.com
Thu Jun 4 14:07:39 CEST 2009

```ok ok I got it...........thank you so much John

RON70 wrote:
>
> Thanks, I did following :
>
> n = 10
> r = 4
> beta = matrix(rnorm(10*4), 4)
> Q = beta[1:r, 1:r]
> P = solve(Q)
> beta.norm = P %*% beta  # This is the normalized, according to you.
>
> Now how can I say "beta" and "beta.norm" are indeed equivalent?
>
> Regards,
>
>
>
>
> John C. Frain wrote:
>>
>> 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
>>>>>
>>>>>
>>>>>
>>>>>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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>>>>>>>
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>>>>>>
>>>>>> _______________________________________________
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>>>>>>
>>>>>
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>>>>>
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>>>>
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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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>
>

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