(G)ARCH estimation. Input series.

After declaring a "default" garch model such as: model = garch(1,1); estimates = estimate(model, y); y should be return series or should it be residuals(squared) from mean models (arima for example)? i think an "offset" option inside model specification could be usefull, but have no clue about it.

Answer 1

[Hang Qian]

Hi Dmitry,

If we have obtained the residuals, then we can create a GARCH model and just estimate the variance equation, like

model = garch(1,1);

estimate(model, y);

Also, we can directly estimate an ARIMA model with GARCH errors, so that both the mean equation and the variable equation are estimated simultaneously. For example,

Mdl = arima(1,0,1);

Mdl.Variance = garch(1,1);

estimate(Mdl,y);

Regards,

Hang Qian