Hi! I need some help regarding estimation of Multivarite GARCH -in mean model , is there any software available that can help ? Specifically I am looking for a solution for trivariate GARCH(1,1) in mean model ....Can any one help.Deb

Hi ssdebThe MBRM software has a demo for multivariate GARCH. It´s in the derivatives module (an EXCEL spreadsheets).S-Plus uses BEKK for this porpouse, I never used s-plus but I read about it.I think the easy way is using "Principal components" to create an orthogonal base from the original system, so you can use Univariate GARCH models. Read the Carol Alexander paper 'Orthogonal GARCH'. It teach you how to apply the method. Or read the multivariate GARCH section in the book "Mastering Risk Vol 2, edited by Carol Alexander. You will find an exellent way to estimate the multivariate GARCH models.The multivariate models are so much harder to implement and the convergence is a common problem.good luck

Just to follow up on javgme's post - standard multivariate ARCH models are really ugly to fit without some pretty strong restrictions on how (usually) the conditional covariances behave. I've never tried a multivariate ARCH in mean model but I can only imagine that it's even more scary. Be that as it may, UCSD have an archive of ARCH related software written in Fortran, Gauss and Matlab. The author of the Matlab stuff is Kevin Sheppard.richg.

ssdeb,I don't recall any canned packages that do multivariate Garch-in-Mean. Certainly, none of the UCSD packages do. It shouldn't be all that ugly to code, though. The decision you must make is the structure of the correlatation matrix in the GARCH process. Its specification will almost single-handedly determine how difficult your estimation is. Don't be deterred by people on this forum regarding multivariate GARCH models. They can be successfully estimated, and are every day. javgome,Although orthogonal GARCH models are easier to estimate than univariate models, they would lose the information that I think forms the crux of ssdeb's question: the impact of the 2nd moment on the first. Think about what it means to estimate a GARCH in mean for one component of an orthogonal decomposition. What does the G-i-M parameter tell you about the underlying processes? Matt.

Deb, I agree with the other replies, that you'll have your hands full with any multivariate GARCH fit unless you can meaningfully specify (i.e., limit) the interaction of the variables in a model. We've found the GARCH package in S-PLUS to be quite good, given the diagnostics and graphical capability that's built in, as well as its ability to handle timeseries flexibly. On the other hand, it's definitely not public-domain software.