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

RON70 ron_michael70 at yahoo.com
Thu Jun 4 14:01:29 CEST 2009

```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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>
>
>
> --
> 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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