A question on VECM

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


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:

-----Urspr?ngliche 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
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