Automatic Identification of Autoregressive Integrated Moving Average Time Series

This paper discusses the development of a computer-oriented technique for automatically identifying nonseasonal Box-Jenkins ARIMA (p, d, q) models or multiplicative seasonal Box-Jenkins ARIMA (p, d, q)∗ (P, D, Q)s models for discrete univariate time series. This technique, called ARIMAID, also provides model parameter estimates so that the output of the system can be directly used for forecasting, control, or simulation purposes. ARIMAID was tested against 46 time series that had either been evaluated using the usual user-interactive procedure or were simulated according to some predefined model. For 45 of these series, ARIMAID made identifications that were statistically equal to or better than recognized manual identifications. Fourteen of the test results are tabulated in the paper. Other applications are also presented to document potential of the identification approach.