I am trying different arch-like models and different $p$, $q$ and $o$ values. If I fit, for example, GJRGARCH with $p=0, q=1, o=1$ I get better results than with any of:
- $p=1, q=1, o=1$;
- $p=0, q=2, o=1$;
- $p=0, q=1, o=2$.
In other words increasing any of the parameters doesn't get parameter with significant p-value and has bigger mean squared error out-of-sample.
On the other hand if I fit model with $p=0, q=2, o=2$ I get that first parameter beta is insignificant but all other are significant plus I get better results out-of-sample.
My question is how should I find the best models, should I just run experiments for all possible combinations (that would take some time) and if yes until what number should I go? Does anyone has any reference for this problem or at least for how far should I go?
