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

RON70 ron_michael70 at yahoo.com
Thu Jun 4 12:40:50 CEST 2009

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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