Is it okay to use AIC to determine the different arima model from different calculation of data?

General
1

So I have used the monthly DJI index adjusted price as my data, and I built up three arima models from the data using log returns, simple returns and the adjusted price respectively.

I knew that generally, the lower the aic, the better the model, but can this apply to my arima model when they came from the same data, but with different calculations?

2

That shouldn't be a problem with the same models, except, possibly, the adjusted price (depending on how it is transformed from returns).

3

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