Combined GARCH((4),0) with hetero statement

[tunelbana2]

Hi,

I have been studing many different statistic packages and so far I didn't find any which could solve my problem.
That's why I decided to write on this forum.
I am trying to estimate univariate GARCH(4,0) model with 4 exogenous variables as below:
Mean equation: X=0
Conditional equation: h= constant+ a1*hetero1(-1)+a2*hetero1(-2)+a3*hetero1(-3)+a4*hetero1(-4)+b1*h(-4)

So in conditional variance equation I have 4 exogenous variables (hetero1 with different lags) and 1 previous value of conditional variance but lagged by 4 days.

The problem is that any software can perform optimization.

Do Rats can solve that problem?
I was browsing automatic window for ARCH/GARCH and I couldn't find the restrictions option. If there be such option, then I will estimate GARCH(4,0) with exogenous variables and restricted GARCH(-1), GARCH(-2) and GARCH(-3) parameters.

Could you please help me with that?

Thanks in advance,
Joanna

[TomDoan]

You would have to use MAXIMIZE to handle that. I'm a bit confused about your model, though. You seem to have a "GARCH" model without any "ARCH", that is, there is no lagged squared residual term. Is that correct?

[tunelbana2]

Hi Tom,

Yes, it looks like I am not using squared residuals. But I am following P. Molnar "High-low range in GARCH models of stock return volatility, where I am introducing Parkinson estimators to conditional variance equations as exogenous variables instead.

Is there any Rats programs for GARCH with exogenous variables and restrictions on parametrers (GARCH(-1 to -3)), or RATS allows to estimete just 4th lag of GARCH proces, without estimating lag first, second and third?

Thanks for your help!
Joanna

[TomDoan]

Nothing that specific. However, the Tsay textbook has quite a few non-standard GARCH models with skipped lags and/or exogenous shifts. tsayp155.rpf and tsayp158.rpf would be the closest to what you're doing.