GARCH(1,1) Coefficients Greater than One

[Michelle]

Dear all,

What should I do when I obtain coefficients of GARCH (1,1) that sum up to more than one?

I would be grateful for your reply.

[trubador]

You can try higher orders (e.g. GARCH(2,1)) or different volatility specifications (e.g. EGARCH, IGARCH). Changing the error distribution or sample period might also help.

[Kavorka]

Trubador said:
"You can try higher orders (e.g. GARCH(2,1))"

I assume that for a GARCH(p,q)-model p is the GARCH-component, and q is the ARCH-component (however, I have also seen the opposite notation).

Question 1. I have absolutely no reason to question that this statement is a valid solution to the problem (since I am very impressed by the staff at EViews). However, could you please give a reference that supports this statement (that this is a good solution to the problem), because the I will use this approach next time.

Question 2. Moreover, what are the stationarity constraints for an GARCH(2,1) model?
I mean, for instance, for a GARCH(1,1) we know that: ... given that alpha=arch-coef., beta=garch-coef., omega=the constant in the variance equation... 0<alpha<1, 0<beta<1, 0<(alpha+beta)<1, omega>0, (omega/(1-alpha-beta))>0... if I remember correctly on the top of my head...
What are the corresponding stationarity (and non-negativity) constraints for a GARCH(2,1) model?

Question 3. Is it the GARCH-component that usually is changed from 1 to 2...or 3, and not the ARCH-component (when we face the problem of violations of the GARCH-parameter constraints)?

Question 4. Are there any drawbacks by specifying the model as GARCH(2,1) instead of GARCH(1,1), except that the interpretation of the estimated coefficients will be complicated and that we lose a d.f.?

Thanks for the advice! Until now I have only concluded that GARCH is a bad specification for the model's DGP and ruled out cond. het. models when the stationarity constraints are not satisfied (or possibly use IGARCH instead), but now I may start to apply GARCH(2,1) instead.

/Pelle