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I want to ask if there is a situation to know the order of GARCH(p, q) from the result. For example, in the case of AR(p), one can know the value of p by plotting pacf(). In case of MA(q), one can know the value of q by plotting acf().

Is there any similar situation to know the value of p and q in GARCH(p, q) models?

May be using Engels Arch Effect test.

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See any standard econometrics textbook on model specification and selection.

One frequently uses terms like AIC, BIC, ... to compute metrics which trade off the improvement in fit that comes from specifying additional terms against the "penalty" (in quotes because how to express this depends on the chosen metric) applied to overly rich models (which may just break). You could test a GARCH(1,1) versus a GARCH(2,1) or GARCH(2,2) this way. As I recall, that is even in the original paper by Bollerslev.

In the wild, you almost never see a GARCH that is not of a GARCH(1,1). Bigger gains can be had by altering the GARCH specifications -- but you have about three decades worth of stuff to read up on now.

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