[Gretl-users] Estimating ARMA model with GARCH errors

[Riccardo Jack Lucchetti]

On Thu, June 8, 2006 03:45, sudip mukherjee wrote:
> Hi,
>
> I want to know how can I estimate the parameters of an
> ARMA(1,1) model with Garch(1,1) errors. I believe all
> the parameters will need to be estimate
> simultaneously.

at present, the only way you have in gretl to estimate an arma model with
garch variance is to use the "mle" command. Section 10.4 in the manual reports
an example with a garch(1,1) model. A simple adaptation of that example
follows:

open djclose
series y = 100*ldiff(djclose)

scalar mu = 0.0
scalar omega = 1
scalar alpha = 0.4
scalar beta = 0.0
scalar phi = 0.0
scalar theta = 0.0

mle ll = -0.5*(log(h) + (e^2)/h)
series e = 0
series e = y - mu - phi*y(-1) - theta*e(-1)
series h = var(y)
series h = omega + alpha*(e(-1))^2 + beta*h(-1)
params mu phi theta omega alpha beta
end mle

Clearly, this is going to "feel" slower than a builtin command, but it should
get the job done.



Riccardo "Jack" Lucchetti
Dipartimento di Economia
Facoltà di Economia "G. Fuà"
Ancona