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I am doing out of sample forecast for my daily exchange rate data. Here I am using different models like ARIMA(0,1,3), ARCH(3), GARCH(1,1), EGARCH(1,1) and TARCH(1,1) with 3 distributions (normal,t and GED).

I want to compare among them using RMSE and MAE to pick up the best model but I noticed that RMSE of ARIMA(0,1,3) is the lowest while the RMSE and MAE of seven other models(ARCH-t, ARCH-ged, GARCH(1,1)-t, GARCH-ged, EGARCH(1,1)-t, TARCH(1,1)-t and TARCH(1,1)-ged) are the same.

So the question here which one should I pick up?

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The selection of the model should obviously be based on data. Divide your data in three parts. Since you have a time series data, you should make the selection like this: $[0,T_1]$ is the model you will use to estimate your model, $[T_1,T_2]$ you may use to choose the best hiperparameters for your model and $[T_2,T_3]$ you may use to select the model. Note that $T_1<T_2<T_3$.

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