# [R-SIG-Finance] [R-sig-finance] Rank

RON70 ron_michael70 at yahoo.com
Fri Jul 3 09:50:40 CEST 2009

```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

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

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. 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.
>
> -----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: 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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```