Dear Mark, Thanks for your response. What is your opinion (other stat-gurus as well)? is there anything wrong in my understanding here?
Regards, "Leeds, Mark (IED)" <[EMAIL PROTECTED]> wrote: hi megh : that material is extremely difficult for me but I would recommend reading one more of the following to get a better idea of cointegration in the multivariate case. Johansen or Hamilton text ( very difficult for me ) Hayashi( less difficult ) Enders ( not difficult ) I think you're A[0] is the pi matrix in the econometric literature. Assuming this is the case ( if not, then Everything below is incorrect and disregard it ) If there are n equations in the system and the rank of pi is n, then there are no cointegrating vectors. If there are n equations and the rank of pi is r, then there are n-r cointegrating vectors. If there are n equations and the and the rank of pi is 1, then there are n-1 cointegrating relationships which is the maximum that there can be. I don't think the rank of pi can be less Than 1 but the determinant of pi can be zero if all it's rows ( columns ) are not linearly independent. This probably doesn't help a heck of a lot but if you want to some other book references, Let me know. A really nice readable explanation of cointegration using the matreix results ( Which I always find difficult ) Is by Lehmann and the title has the work "desiderata" in it. I don't have it in front of me But if you google "lehmann desiderata", I'm sure it will pop up. -----Original Message----- From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED] On Behalf Of Megh Dal Sent: Sunday, August 05, 2007 6:33 AM To: r-help@stat.math.ethz.ch Subject: [R] Understanding of Johansen test. Dear all, I am struggling to understand the johansen test procedure in the context of co-integration in time series. Yes I understand that this forum is not directly statistics related but still I am posting here hoping that I would get som help. The error correction representation of a VAR[p] model can be written as: Delta y[t] = A[0]*y[t-1] + A[1]*Delta y[t-1] +.............. where, y[t] is a vector of n variables. It is said that "if the variables in system are all co-integrated, then Rank of A[0] will be different from zero" My understanding is following : suppose, y[t] is of order 3 and p = 1 Then Delta y[t] = A[0]*y[t-1] + epsilon[t] Hence : Delta y1[t] = a[11]*y1[t-1] + a[12]*y1[t-1] +a[13]*y1[t-1] + epsilon1[t] Delta y2[t] = a[12]*y1[t-1] + a[22]*y1[t-1] +a[23]*y1[t-1] + epsilon2[t] Delta y3[t] = a[31]*y1[t-1] + a[32]*y1[t-1] +a[33]*y1[t-1] + epsilon3[t] But is rank of A[0] is 0 then it is possible to find non-zero coef for all of above three equations such that : a[11]*y1[t-1] + a[12]*y1[t-1] +a[13]*y1[t-1] = 0 a[12]*y1[t-1] + a[22]*y1[t-1] +a[23]*y1[t-1] = 0 a[12]*y1[t-1] + a[22]*y1[t-1] +a[23]*y1[t-1] = 0 therefore number of co-integrating relationship is 3 am I correct? Therefore in my understanding : if variables in a system show some co-integrating relationship thenrank should be close to zero. Am I making any mistakes? Can anyone here clarify me? Regards, Megh --------------------------------- [[alternative HTML version deleted]] ______________________________________________ R-help@stat.math.ethz.ch mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code. -------------------------------------------------------- This is not an offer (or solicitation of an offer) to buy/se...{{dropped}} ______________________________________________ R-help@stat.math.ethz.ch mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
