How is the difference level in ARIMA models determined?

The determination of the difference level in ARIMA models is crucial for ensuring that the time series data is stationary. In this context, the KPSS unit-root test serves this purpose effectively. The KPSS test specifically analyzes the null hypothesis that an observable time series is stationary around a deterministic trend, which helps to identify whether differencing is needed to achieve stationarity.

When applying ARIMA models, it's essential to ensure the data does not have unit roots, as non-stationary data can lead to unreliable and spurious results. The KPSS test provides a systematic approach to evaluate the presence of a unit root, thereby guiding analysts in selecting the appropriate differencing level to apply.

While historical trends can inform the overall behavior of the data, and regression analysis can model relationships between variables, these methods do not directly assess the stationarity of individual time series. The calculation of AIC values, although useful for model selection, occurs after the model structure has been determined and does not directly address how to identify the necessary differencing level to stabilize the data.