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

RON70 ron_michael70 at yahoo.com
Fri Jul 3 18:29:14 CEST 2009

```Oh John, it is page 399, sorry.

John C. Frain wrote:
>
> 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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>>>> > 18:06:00
>>>> >
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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
>
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