Autoregressive integrated moving average (ARIMA) forecasting methods were popularized by G. E. P. Box and G. M. Jenkins in the 1970s. These techniques, often called the Box-Jenkins forecasting methodology, have the following steps:
Model identification and selection
Estimation of autoregressive (AR), integration or differencing (I), and moving average (MA) parameters
Model checking
ARIMA is a univariate process. Current values of a data series are correlated with past values in the same series to produce the AR component, also known as p. Current values of a random error term are correlated with past values to produce the MA component, q. Mean and variance values of current and past data are assumed to be stationary, unchanged over time. If necessary, an I component (symbolized by d) is added to correct for a lack of stationarity through differencing.
In a non-seasonal ARIMA(p,d,q) model, p indicates the number or order of AR terms, d indicates the number or order of differences, and q indicates the number or order of MA terms. The p, d, and q parameters are integers equal to or greater than 0.
Cyclical or seasonal data values are is indicated by a seasonal ARIMA model of the format
SARIMA(p,d,q)(P,D,Q)(t)
The second group of parameters in parentheses are the seasonal values. Seasonal ARIMA models consider the number of time periods in a cycle as defined in the Historical Data – Seasonality dialog (Figure 2, Historical Data – Seasonality Dialog). For a year, the number of time periods (t) is 12.
Note: | In the Predictor user interface, seasonal ARIMA models do not include the (t) component, although it is still used in calculations. See the Bibliography for references that describe this methodology in more detail. Crystal Ball ARIMA models do not fit to constant datasets or datasets that can be transformed to constant datasets by non-seasonal or seasonal differencing. Because of that feature, all constant series, or series with absolute regularity such as data representing a straight line or a saw-tooth plot, do not return an ARIMA model fit. |
To use ARIMA methods:
In the Autoregressive Integrated Moving Average (ARIMA) Details panel, select Automatic (the default) or Custom models.
Note:
Unless you are thoroughly acquainted with ARIMA methodology and intend to construct or use existing custom ARIMA models, select Automatic.
Optional: If you selected Automatic, select a model selection criterion, Minimize information criterion (the default) or Minimize selected error measure. The default generally provides a better ARIMA estimate. Minimizing the error measure selected elsewhere for Predictor forecasting can result in overfitting.
Optional: Click Select Information Criterion (Alt+e) to indicate which information criterion to use. For details, see Selecting an ARIMA Model Selection Criterion. Unless you have good reason to select another, BIC (the default) is usually appropriate.
Optional: Select Perform extended model search to compare more models to the historical data. Results may be somewhat more accurate, but the analysis can take noticeably more time.
Optional: If you selected Custom models in step 2, build a list of models to use. For instructions, see Using ARIMA Custom Models.
Optional: Click ARIMA Options (Alt+o) to indicate whether to include a constant in the ARIMA equation and whether to perform a Box-Cox transformation. The default, AutoSelect or None, is usually appropriate for both options. For more information, see Setting ARIMA Options.
Note: | If Automatic is selected, any displayed models are fitted to each series. Custom seasonal models are not fitted to non-seasonal series, but non-seasonal models will be fitted to seasonal series. If Custom models is selected, models apply only to the currently selected Predictor series and must be defined for each series separately. |