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:
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