Time series forecasting is a difficult problem with no easy answer. There are countless statistical models that claim to outperform each other, yet it is never clear which model is best.
That being said, SARIMA-based models are often a good model to start with. They can achieve decent scores on most time-series problems and are well-suited as a baseline model in any time series problem.
The ARIMA model is great, but to include seasonality and exogenous variables in the model can be extremely powerful. Since the ARIMA model assumes that the time series is stationary, we need to use a different model.
SARIMA Formula — By Author
Enter SARIMA (Seasonal ARIMA). This model is very similar to the ARIMA model, except that there is an additional set of autoregressive and moving average components.The additional lags are offset by the frequency of seasonality (ex. 12 — monthly, 24 — hourly).
SARIMA models allow for differencing data by seasonal frequency, yet also by non-seasonal differencing. Knowing which parameters are best can be made easier through automatic parameter search frameworks such as pmdarina.
Sarimax Formula — By Author
Above is the the of the SARIMAX model. This model takes into account exogenous variables, or in other words, use external data in our forecast. Some real-world examples of exogenous variables include gold price, oil price, outdoor temperature, exchange rate.
It is interesting to think that all exogenous factors are still technically indirectly modeled in the historical model forecast. That being said, if we include external data, the model will respond much quicker to its affect than if we rely on the influence of lagging terms.