The Three Stages of ARIMA Modeling
The analysis performed by PROC ARIMA is divided into three stages,
corresponding to the stages described by Box and Jenkins (1976).
The IDENTIFY, ESTIMATE, and FORECAST
statements perform these three stages, which are summarized below.
- In the identification stage, you
use the IDENTIFY statement to specify the response series
and identify candidate ARIMA models for it.
The IDENTIFY statement reads time series that are to be
used in later statements, possibly differencing them, and computes
autocorrelations, inverse autocorrelations, partial autocorrelations,
and cross correlations. Stationarity tests can be performed to
determine if differencing is necessary.
The analysis of the IDENTIFY statement output usually suggests one or
more ARIMA models that could be fit. Options allow you to test for
stationarity and tentative ARMA order identification.
- In the estimation and diagnostic checking stage, you
use the ESTIMATE statement to specify the ARIMA model to fit
to the variable specified in the previous IDENTIFY statement,
and to estimate the parameters of that model.
The ESTIMATE statement also produces diagnostic statistics to help
you judge the adequacy of the model.
Significance tests for parameter estimates
indicate whether some terms in the model may be unnecessary.
Goodness-of-fit statistics aid in comparing this model to others.
Tests for white noise residuals indicate whether the residual series
contains additional information that might be utilized by a more complex model.
If the diagnostic tests indicate problems with the model,
you try another model, then repeat the estimation and diagnostic checking stage.
- In the forecasting stage you
use the FORECAST statement to forecast future values of the time series
and to generate confidence intervals for these forecasts
from the ARIMA model produced by the preceding ESTIMATE statement.
These three steps are explained further and illustrated through an
extended example in the following sections.
Copyright © 1999 by SAS Institute Inc., Cary, NC, USA. All rights reserved.