Selecting the Order of a GARCH Model

Summary

The question asks whether GARCH orders can be identified from plots in the way autoregressive and moving-average orders are often explored with partial and ordinary autocorrelation functions. The answer recommends information criteria such as AIC or BIC for comparing candidate specifications. These criteria balance improvement in fit against a penalty for adding parameters, so a researcher can compare models with different lag structures.

The response gives comparisons such as a GARCH(1,1) against larger alternatives as examples, and says the ARCH effect test is not the proposed way to determine both orders. It also offers a practical observation that GARCH(1,1) is commonly used, while noting that changes to the model specification may be more valuable than simply increasing its order. No data, selection results, or detailed fitting procedure are provided, so candidate order choice still depends on the series and the modeling objective.

Key ideas

• Use criteria such as AIC or BIC to compare candidate GARCH orders.
• Information criteria weigh fit improvement against a penalty for model complexity.
• Autocorrelation plots for AR and MA models are not presented as a direct GARCH order rule.
• GARCH(1,1) is described as a common specification, though alternative model forms may be worth considering.

Tags

# knowing the order of GARCH model


# knowing the order of GARCH model












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.

## Answer by Dirk Eddelbuettel (score 6)

https://quant.stackexchange.com/a/7951

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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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.