Mark, statquant2 As I understand the question it is not to test if a VAR is stable but how to construct a VAR that is stable and automatically satisfies the condition Mark has taken from Lutkohl. The algorithm that I have set out will automatically satisfy that condition.The matrix that should be "estimated by the algorithm is A on the last line of page 15 of Lutkepohl. Incidentally the corresponding matrix for the example on page 15 is singular. The algorithm that I have set out will only lead to systems with a non-singular matrix.
I still don't see how a matrix generated in this way corresponds to a real economic system. Of course you may have some other constraints in mind that would make the generated system correspond to something more real. John On Saturday, 14 January 2012, Mark Leeds <marklee...@gmail.com> wrote: > Hi statquant2 and john: In the first chapter of Lutkepohl, it is shown that stability f > a VAR(p) is the same as > > det(I_k - A1z - .... Ap Z^p ) does not equal zero for z < 1. > > where I_k - A1z - ... Ap z^p is referred to as the reverse characteristic polynomial. > > So, statquant2, given your A's, one way to do it but be would be to check the roots of the > polynomial implied by taking the determinant of the your polynomial. > > There's an example on pg 17 of lutkepohl if you have it. If you don't, I can fax it to you > over the weekend if you want it. > > > > On Fri, Jan 13, 2012 at 8:34 PM, John C Frain <fra...@gmail.com> wrote: >> >> I think that you must approach this in a different way. >> >> 1 Draw a set of random eigenvalues with modulus < 1 >> 2 Draw a set of random eigenvalues vectors. >> 3 From these you can, with some matrix manipulations, derive the >> corresponding Var coefficients. >> >> If your original coefficients were drawn at random I suspect that the VAR >> would not be stable. I am curious about what you are trying to do. >> >> John >> >> On Friday, 13 January 2012, statquant2 <statqu...@gmail.com> wrote: >> > Hello Paul >> > Thanks for the answer but my point is not how to simulate a VAR(p) process >> > and check that it is stable. >> > My question is more how can I generate a VAR(p) such that I already know >> > that it is stable. >> > >> > We know a condition that assure that it is stable (see first message) but >> > this is not a condition on coefficients etc... >> > What I want is >> > generate say a 1000 random VAR(3) processes over say 500 time periods that >> > will be STABLE (meaning If I run stability() all will pass the test) >> > >> > When I try to do that it seems that none of the VAR I am generating pass >> > this test, so I assume that the class of stable VAR(p) is very small >> > compared to the whole VAR(p) process. >> > >> > >> > >> > -- >> > View this message in context: >> http://r.789695.n4.nabble.com/simulating-stable-VAR-process-tp4261177p4291835.html >> > Sent from the R help mailing list archive at Nabble.com. >> > >> > ______________________________________________ >> > R-help@r-project.org 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. >> > >> >> -- >> John C Frain >> Economics Department >> Trinity College Dublin >> Dublin 2 >> Ireland >> www.tcd.ie/Economics/staff/frainj/home.html >> mailto:fra...@tcd.ie >> mailto:fra...@gmail.com >> >> [[alternative HTML version deleted]] >> >> ______________________________________________ >> R-help@r-project.org 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. > > -- John C Frain Economics Department Trinity College Dublin Dublin 2 Ireland www.tcd.ie/Economics/staff/frainj/home.html mailto:fra...@tcd.ie mailto:fra...@gmail.com [[alternative HTML version deleted]] ______________________________________________ R-help@r-project.org 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.
