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Re: [R-sig-finance] Rank
by RON70
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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
y[t] = alpha * t(beta) * (y[t-1] : x[t-1]) + ..................
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. 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
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
y[t] = alpha * t(beta) * (y[t-1] : x[t-1]) + ..................
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. 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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