Re: [Gretl-users] convergence of ARMA and GARCH models
On Wed, 27 Oct 2004, Allin Cottrell wrote:
On Tue, 26 Oct 2004, Blaise Roncagli wrote:
> Thanks for the quick response. I have attached a dataset called
> "sampledata.xls"...
I'm currently trying to do a comparison of GARCH results from gretl
and R (the ARMA results seem pretty much the same).
My problem at present is that I can't get R to produce any sensible
GARCH estimates. I'm using R 2.0.0 on Linux, with the "tseries"
library version 0.9-23. With Blaise's two series, and also with the
benchmark Bollerslev-Ghysels dataset, the GARCH "a1" and "b1"
estimates are printed as "0.050000", regardless of the particular
series used. (I have printed the series out from R to check that
the data are right.) The B-G results do not remotely resemble the
benchmark results.
Folks, I'm attaching a file that pretty much explains what the trouble
with TBILL is: for a Garch(1,1) you have 4 parameters:
y_t = k + e_t
v(e_t) = \omega + a e_{t-1}^2 + b v(e_{t-1})
Where v(.) = conditional variance.
I run a little experiment:
1) keep k fixed at sample mean of y
2) keep omega at (sample variance)*(1-a-b)
3) plot the likelihood for all admissible values of a and b (grid width =
0.1)
As you can see by the attached files, this is one of the rare (but not
exceptional) cases when the sample likelihood doesn't have a maximum in
the interior of the parameter space.
It must be said that the original series looks very much I(1), so applying
a garch model to the TBILL series is rather meaningless anyway.
Riccardo `Jack' Lucchetti
Dipartimento di Economia
Università di Ancona
jack(a)dea.unian.it
http://www.econ.unian.it/lucchetti
Attachments:
- Loglikelihood.zip (application/zip — 152.2 KB)