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Re: [R-sig-finance] Rank

by RON70 :: Rate this Message:

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@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.
> >
> > -----Ursprüngliche Nachricht-----
> > Von: r-sig-finance-bounces@stat.math.ethz.ch
> > [mailto:r-sig-finance-bounces@stat.math.ethz.ch] Im Auftrag von RON70
> > Gesendet: Freitag, 3. Juli 2009 03:22
> > An: r-sig-finance@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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> >
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