Great questions, thanks for asking!
- ARIMA is just a general name for a whole family of models, starting from simple auto-regressions (AR-models) and moving averages (MA-models) and going deeper into ARIMA, SARIMA, and SARIMAX models, depending on the specifications and parameters. But overall, SARIMAX model still has the very same parameters among all others — p, q, and d as a simple ARIMA model has
- I agree, the model might not be the best possible for this particular time-series data, however, it is the best model in terms of quality among other possible combinations of parameters, which we iteratively checked during the `optimizeSARIMA` procedure. The fact, that AIC is around thousands does not tell us anything about the quality of the model by itself. It is not an interpretable metrics and is used only for model selection — that is comparison of multiple models and selecting the one with the minimal AIC value. Basically, that is how we selected our final specifications for the model among all other possible parameter combinations. P-value indicates, that some of the factors in our model might be statistically insignificant, however, the residual plot indicates, that this specification of the model results with a stationary distribution of the residuals with no significant autocorrelations, so the model can be used to make unbiased predictions. Finally, the Dickey-Fuller test is used only to check stationarity of the data that goes into the model (needed for the model assumptions) and the residuals that come out of the model (needed to understand if the model is correct). In both cases we see that after all data transformations and with selected parameters we have stationary time-series data
- Actually, we do use stationary time-series for the model. You may notice that both parameters d and D were fixed and were equal 1. That is because during data exploration we found out that taking first order differences, both seasonal and non-seasonal, provide us with a clean stationary data, without any trends. Hence, we set those parameters in the model and all transformations are applied accordingly
Hope that helps!