Forecast with AR, MA and ARIMA models look all equal and false

Thanks a lot technocrat for your answer,

maybe one (hopefully) last question. You said that I should make the data stationary before applying the ARIMA models. But does the ARIMA models not do this themselves? As far as I understood in ARIMA(p,d,q) models the d part stands for differencing to make a time series stationary.

Good catch. Yes, although sometimes we want to tweak the ARIMA arguments manually. My reason is that if we know there is auto-correlation and want to compare models, they should all be on a common footing with first-order differencing. However, I did not check to see if ARIMA takes differenced data and re-differences them, but probably not.

Thanks technocrat for your answer once again,

I have to admit that I do not really understand your last post. So did you basically make the time series stationary before applying the ARIMA approach? As said before, when you input your time series to ARIMA it should basically make it automatically stationary (either through AUTOARIMA or the H-K algorithm, as far as I understood). So when making the time series stationary before the input then applying those methods would yield a second iteration of making it stationary and I can imagine that this might yield worse results.

I checked it and for ARIMA with my data, the differenced data input and un-differenced had the same result. Let me know if that's not your experience.