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I am a beginner to econometrics and STATA, so I would like to apologise if this is a bad question, but have accidentally dwelled down into volatility modeling. I have come to understand that the standard model to use is GARCH(1,1), which I have noted has a very similar form to ARMA(1,1) with the transform of $y_t \rightarrow y_t^2$ (as also noted by: What is the difference between GARCH and ARMA? )

My question is, would it be invalid to use an ARMA(1,1) instead of GARCH(1,1) if I am purely interested in the volatility series? (Although this might be wrong) my impression is that STATA has more flexibility with respect to the addition of exogenous regressors and tests for ARMA than for GARCH hence the attraction of using it.

Jhonny
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  • Would you use ARMA on $y_t$ or on $y_t^2$? – Richard Hardy May 04 '19 at 10:40
  • I was thinking $y_t^2$ – Jhonny May 04 '19 at 13:30
  • The purpose behind the GARCH equation is to provide a description for the error term $\varepsilon_t$, not the entire series $y_t$. A trivial example would be the case where there is no mean or trend in $y_t$ in which case it is simply $y_t = \varepsilon_t$ and then you can apply GARCH "directly" to the series, if that's what you meant. – Emil May 04 '19 at 15:16

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