ARIMA in Python: Endogenous versus Exogenous Variables

The ARIMA model in statsmodels is described here.

Its constructor has the following initial arguments: ARIMA( endog, exog=None, order=(0,0,0),....).

• endog - observed time series process, y
• exog - array of "exogenous regressors"
• order - (p, d, q) model for autoregressive, differences and moving average component

Exogeneous regressors are added to the ARIMA equation where external variables may have some forecasting power. For example, electricity demand could utilise temperature as an exogenous variable.

The (p, d, q) component specification can be said to be the true "spirit" of ARIMA.

ARIMA methods were created by George Box and Gwilym Jenkins and are hence sometimes called  Box-Jenkins methods.

SARIMA extends this to Seasonal Data, where seasonal differencing is used to create stationarity.