Rank

Your pi matrix is 2 by 5 and therefore must be of rank <= 2 and you
can not have more than two cointegrating relationships betwween the
y's.   Page 408 of my copy of Lutkepohl(2005) deals with Multiplier
analysis and Optimal Control

Best Regards

John

2009/7/3 RON70 <ron_michael70 at yahoo.com>:

I am not sure why you are saying c.i. relationships can not be more than
n.
Quote from Lutkepohl, page : 408 : "Because the error correction term now
involves all the cointegration relations between the endogenous and
unmodelled variables,it is possible that r>K. ", here he defined K as
number
of endo. variables in the system................any idea?

However your 1st point is valid, I should have added diff. operator on
the
left side, it was a typo.

PS. I understand some ppl here previously suggested not to read Lutkepohl
1st, however except few things I am getting comfortable-reading on that,
atleast easier than Hamilton, perhaps I have only softcopy of Hamilton
;).


matifou wrote:

2009/7/3 RON70 <ron_michael70 at yahoo.com>

This is a finance related question in the sense that I have come
accross
this
kind of problem in Co-Integration matrix construction in a VECM. I am
explaing how :

Suppose I have 2 endogeneous variables and 3 exogeneous variable all
are
I(1) and assumed to have cointegration relationships among them. Let
say
the
DGP is

what do you mean by exogenous?

y[t] = alpha * t(beta) * (y[t-1] : x[t-1]) + ..................

left should be differenced

pi = alpha * t(beta)

Obviously dimension of y vector is 2 and x vector is 3. Therefore there
could be more than 2 cointegrating relationships in that.

if you have more than two cointegrating relationships: I would say x is
not
exogeneous

Hence rank of pi

is in principle more than 2. As number of co-integrating relationships
is
estimated on looking at rank of pi matrix. However number of rows there
is
:
2.

I am trying to understand this scenario here. In this case, can usual

VECM estimation procedure work? More important to me is to understand
rank
of pi is more than it's row number.

Thanks





Enrico Schumann wrote:

that's not a finance question, but the rank can at most be the min of

n

and
m.

-----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: Freitag, 3. Juli 2009 03:22
An: r-sig-finance at stat.math.ethz.ch
Betreff: [R-SIG-Finance] [R-sig-finance] Rank


Hi, i have a small matrix related question which most of you find

trivial

however I am not getting through. Suppose I have a matrix of

dimension

(nxm), n < m. Is it in principle possible to have the rank of that

matrix

greater than n? Is it possible to have some example?

Thanks,
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John C Frain, Ph.D.
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