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I stumbled upon a problem regarding model selection based on AIC. For forecasting purposes I want to select the model with the lowest AIC. I first fitted an ARIMA model and obtained AIC_arima = -952.37.

After that, I wanted to see how a ARIMA-GARCH model would compare against this. To fit the model I used ugarchfit() function from the 'rugarch' package in R. The parameters are chosen in such a way that the AIC is minimized.

Strangely, the AIC is now -3.4688 indicating the ARIMA model was MUCH better than ARIMA-GARCH, which I thought was too big of a difference. I took a deeper look and found this:

enter image description here As the AIC is calculated as:

AIC= 2*k - 2*logLik, where k is the number of parameters estimated.

Shouldn't the output be AIC = 2*9 - 2*510.2484 = -1002.4968, resulting in the selection of ARIMA-GARCH?

Hopefully someone can help me out where I went wrong.

Kind regards, T Goose

T Goose
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    This post should help you out: https://stats.stackexchange.com/questions/100003/cannot-replicate-the-aic-in-a-garch-model – Kidae Kim Oct 15 '19 at 08:52
  • Thank you for your reply. So it is the -3.4688, but then my question is how can the criteria decrease so much? The residuals after fitting ARIMA-GARCH are White Noise so the model fits quite good I would say. – T Goose Oct 15 '19 at 08:58
  • Nevermind, I think I should calculate the AIC in ARIMA the same way as they do in 'rugarch' (the AIC is scaled by N, at least that's how I interpreted the other post). – T Goose Oct 15 '19 at 09:01

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