linear regression with GARCH/EGARCH errors

I need to estimate a linear model with GARCH or EGARCH errors:

    mean eqn: Y = c +b1X1 +b2X2 + e    e_t ~ N(0,sigma_t^2)

    vol  eqn: sigma_t^2 follows GARCH or EGARCH

I have written the likelihood function and optimise it. I would prefer to use built-in matlab functions to estimate it (as a check).

any guidance appreciated!

Answer 1

[Philip]

with a little guidance from Mathworks support, my PhD student solved this problem.

Use the "estimate" syntax to estimate a garch (1,1) or egarch(1,1) model.

    Mdl = arima('Variance',egarch(1,1));

this seems to "turn off" the lagged AR terms in the conditional mean, but still allows e/garch in the conditional variance.

then, it's just a matter of:

   [EstMdl,EstParamCov,logL,info] = estimate(Mdl,Y,'X',X);

The "X" tells matlab to expect a matrix of exogenous regressors. No need to include a vector of ones in X, since an intercept comes as standard in the "estimate" routine.

[aa ee]

Thanks very much for the answer. Do you know how to extract the standard errors of estimated parameters?? Matlab "print" function explains very little on this matter.

Answer 2

[the cyclist]

Do you have the Econometrics Toolbox? A garch() function is available in it. Here's a link to the documentation.

[Philip]

Yes, I have all the toolboxes. I have used garch() to fit a model, perhaps with a constant mu in the mean. My uncertainty surrounds how to get the conditioning variables (i.e,., regressors c + b1*X1 + b2*X2) in the mean equn.

Answer 3

[Adriano]

How can i extract the e vector? Thanks!