[Gretl-users] arima + arch ?

[Riccardo (Jack) Lucchetti]

On Thu, 7 Jun 2007, Chris wrote:

> Hi,
>
> The actual model isn't just based on the Y variable, it's of the form y = B1
> + B2*X2 + B3*X3 . in your example you seem to generate only a Y variable and
> doing everything with the Y variable. I think the major problem here is I
> may not be understanding what I'm doing;) in gretl, when you run an arima
> model it estimates a bunch of stuff (the arima process) and then estimates
> the betas on your other explanatory variables. The same happens when you
> estimate a garch process. The output for the script only generates estimates
> of the arma process variables and the garch process variables. I'm trying to
> figure out how to estimate the coefficients on the other explanatory
> variables as well...

That's easy-peasy: when you compute the forecast errors e, just subtract 
from y the conditional mean too; clearly, you'll need to include the 
regressors as additional parameters to the function, as in

function filter(series y, series x, \
         scalar b, scalar arpar, scalar mapar, \
         scalar om, scalar alpha, scalar beta, \
         series *e, series *h)

   scalar err = 0
   scalar T = $nobs
   series e = 0
   series h = om/(1-alpha-beta)

   loop for i=2..T --quiet
     scalar e2lag = e[i-1]^2
# note the change here
     e[i] = y[i] - (x[i]*b + arpar*y[i-1] + mapar*e[i-1])
     h[i] = om + alpha*e2lag + beta*h[i-1]
   end loop

   return scalar err

end function

Better still, you may want to specify x as a list (or a matrix) and b as a 
vector.

Maybe it's time to get hold of a good econometrics textbook? ;-)


Riccardo (Jack) Lucchetti
Dipartimento di Economia
Università Politecnica delle Marche

r.lucchetti at univpm.it
http://www.econ.univpm.it/lucchetti