Auto Arima

Identifying the optimal parameters for an Arima model manually is a very time-consuming process. The Auto Arima algorithm automatically identifies the most optimal parameters for an Arima model:

• The order of differencing (d) is identified by conducting repeated differencing tests, such as Kwiatkowski–Phillips–Schmidt–Shin (KPSS).

• The value of the autoregressive order (p) and the order of the moving average (q) are chosen by optimizing an information criterion, such as akaike information criterion or bayesian information criterion. The algorithm uses a stepwise search to traverse the model space, rather than testing every possible combination of the possible parameters p and q. This process is extended to identify the optimal order of the seasonal autoregressive order (P), seasonal difference order (D) and seasonal moving average order (Q) if required.

In Demand Modeler, ArimaX is an identical estimator with AutoArima in case there are no external features incorporated in the model.

This algorithm is most effective when:

• The time series length is short to medium (20 to 50 points), although it can also work well on longer time series.

• Causal data is not available.

• The time-series is non-stationary. Auto Arima can accommodate this by first making it stationary.

• An older lag (lag 5) is more important than a newer lag (lag 3), in which case the algorithm can assign appropriate weights. Exponential smoothing will always assign a higher weight to lag 3 than to lag 5.