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

[John Frain]

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.
>>> >
>>> > -----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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>>
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>
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-- 
John C Frain, Ph.D.
Trinity College Dublin
Dublin 2
Ireland
www.tcd.ie/Economics/staff/frainj/home.htm
mailto:frainj at tcd.ie
mailto:frainj at gmail.com