regression with ARMA_GARCH errors

I want to estimate a regression model with ARMA(3,3) - GARCH(1,1) errors:

y_t = bX_t + e_t

e_t = a_1e_{t-1}+...+a_3e_{t-3} + u_t + r_1u_{t-1}+...+r_3u_{t-3}

u_t = h_tε_t

h_t = ω + αu^2_{t-1} + βh_{t-1}

I know I can do it in two steps. Estimate the regression first and then fit an ARMA model with GARCH variance to the residuals of the regression, however I was wondering If I could do it in one step. The obvious choice would be a regARIMA model but regARIMA model doesn't support garch(1,1) value in 'Variance'.

Thank in advance

[Giovambattista Perciaccante]

suppose your observed variable is called:

 yt

specify the model for the conditional variance as GARCH(1,1)

 varmdl = garch('GARCHLags', 1, 'ARCHLags', 1)

You haven't estimated anithing yet.

Then specify the model for the mean as ARMA(3,3). Inside the function ARIMA you call the model for the variance specifying the option 'Variance'

 mdl = arima('ARLags',3, 'MALags',3,'Variance', varmdl)

Again you haven't estimated anything yet.

Finally using the function ESTIMATE you estimate all the coefficients in one go:

 es = estimate(mdl, yt)

[Manthos Vogiatzoglou]

Thanks a lot!

Merry Christmas