gotcha john. thanks.
On Sat, Jan 14, 2012 at 9:28 PM, John C Frain <fra...@gmail.com> wrote: > Mark > > This should be reasonably straightforward. In the simplest case you wih to > draw a random complex number in the unit circle. This is best done in polar > coordinates. > > If r is a random mumber on (0,1) and theta a random number on (0, 2 Pi) > then if x=r cos(theta) and y= r sin(theta), x + i y is inside the unit > circle. As such roots come in conjugate pairs a second is x-iy. If you > then need an odd number of roots the final can simply be a random number on > (0,1). You do not need to use a uniform distribution but can use any > distribution on the required intervals or restrain more or the eigenvalues > to be real. > > John > > On Sunday, 15 January 2012, Mark Leeds <marklee...@gmail.com> wrote: > > hi john. I think I follow you. but , in your algorithm, it is > straightforward to > > generate a set of eigenvalues with modulus less than 1 ? thanks. > > > > > > On Sat, Jan 14, 2012 at 5:31 PM, John C Frain <fra...@gmail.com> wrote: > > > > 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 > >>> > > -- > 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.
