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

[RON70]

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.
>> >
>> > -----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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