Re: [R-sig-finance] Rank

>
> 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@...>
>>
>>>
>>> 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@...
>>> > [mailto:r-sig-finance-bounces@...] Im Auftrag von RON70
>>> > Gesendet: Freitag, 3. Juli 2009 03:22
>>> > An: r-sig-finance@...
>>> > 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,
>>> > --
>>> > View this message in context:
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>>> >
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>>> > 18:06:00
>>> >
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>>
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