MV GARCH w MAXIMIZE, t-distribution?

[Lassemaja]

Dear All,

I'm estimating a trivariate MV GARCH model using MAXIMIZE, because the built-in GARCH is not general enough for my model (e.g. different specifications of the three variance equations). Now, my data seem to require a t-distribution. I have managed to alter the line "%logdensity(hx,ux)" from the GARCHMV.prg file to "%logtdensity(hx,ux,nu)", where "nu" is a fixed df, with success (compared with the built-in procedure for a simpler version of my model). Is there a way to estimate the df parameter alongside the rest of the model parameters, like in the built-in procedure?

Thanks in advance!

Best regards,
Lars

[TomDoan]

Just add NU to the parameter set. Probably give it a guess value of something like 20 (sort of Normal, but not too far from fatter tails).

[Lassemaja]

Thanks! That was easy... and worked perfectly! As a follow-up question: is there an equally easy way to allow for different t-distributions across equations, i.e. a specific df-parameter for each of the three residuals' distributions? My "problem" seems to be that one of my time series is far more non-normal than the other two... I think I've seen it done somewhere, but I can't remember the reference right now.

Best,
Lars

[TomDoan]

A joint covariance matrix with different marginal t's? I'm not sure I've ever seen anything like that. I certainly don't think it would be "easy."

[Lassemaja]

OK... one example would be Masulis and Ng, "Overnight and daytime stock-return dynamics on the LSE: the impacts of the big bang and the 1987 stock-market crash", Journal of Business and Economic Statistics 13, 1995, 365-378. They estimate a 2-variable GARCH model with cross-equation shock dependences in the variance equations, and one t-distribution per shock, where each df parameter equals 5+30(1-(1+exp(-10(theta-0.5)))^-1)), theta is a parameter to estimate, and the functunal form puts restrictions on the df parameter. I agree, there model is not standard, but looks alright to me