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The ARIMA Procedure
The ARIMA procedure provides the identification, parameter estimation, and forecasting of autoregressive integrated moving average (Box-Jenkins) models, seasonal ARIMA models, transfer function models, and intervention models.
The ARIMA procedure offers complete ARIMA (Box-Jenkins) modeling with no limits on the order of autoregressive or moving average processes. Estimation can be done by exact maximum likelihood, conditional least squares, or unconditional least squares. In addition you can model intervention models, regression models with ARMA errors, transfer function models with fully general rational transfer functions, and seasonal ARIMA models. PROC ARIMA's model identification diagnostics include plots of autocorrelation, partial autocorrelation, inverse autocorrelation, and cross-correlation functions.
PROC ARIMA also allows tentative autoregressive moving average (ARMA) order identification based on smallest canonical correlation, extended sample autocorrelation function, or information criterion analysis. ARIMA model-based interpolation of missing values is permitted. Forecasting is tied to parameter estimation methods. Finite memory forecasts are used for models estimated by maximum likelihood or exact nonlinear least squares, while infinite memory forecasts are used for models estimated by conditional least squares.
The ARIMA procedure offers a variety of model diagnostic statistics, including
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Akaike's information criterion (AIC)
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Schwarz's Bayesian criterion (SBC or BIC)
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Ljung-Box chi-square test statistics for white noise residuals
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stationarity tests, including Augmented Dickey-Fuller (including seasonal unit root testing), Phillips-Perron, and random-walk with drift tests
The %DFTEST macro performs Dickey-Fuller tests for simple unit roots or seasonal unit roots in a time series. The %DFTEST macro is useful to test for stationarity and determine the order of differencing needed for the ARIMA modeling of a time series.
For further details, see the SAS/ETS® User's Guide: The ARIMA Procedure.
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Examples
- Simulated IMA Model
- Seasonal Model for the Airline Series
- Model for Series J Data from Box and Jenkins
- An Intervention Model for Ozone Data
- Using Diagnostics to Identify ARIMA Models
- Detection of Level Changes in the Nile River Data
- Iterative Outlier Detection
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