Overview (AREG command)

AREG estimates a regression model with AR(1) (first-order autoregressive) errors. (Models whose errors follow a general ARIMA process can be estimated using the ARIMA procedure.) AREG provides a choice among three estimation techniques.

For the Prais-Winsten and Cochrane-Orcutt estimation methods (keywords PW and CO), you can obtain the rho values and statistics at each iteration, and regression statistics for the ordinary least-square and final Prais-Winsten or Cochrane-Orcutt estimates. For the maximum-likelihood method (keyword ML), you can obtain the adjusted sum of squares and Marquardt constant at each iteration and, for the final parameter estimates, regression statistics, correlation and covariance matrices, Akaike’s information criterion (AIC) ¹, and Schwartz’s Bayesian criterion (SBC) ².

Options

Estimation Technique. You can select one of three available estimation techniques (Prais-Winsten, Cochrane-Orcutt, or exact maximum-likelihood) on the METHOD subcommand. You can request regression through the origin or inclusion of a constant in the model by specifying NOCONSTANT or CONSTANT to override the setting on the TSET command.

Rho Value. You can specify the value to be used as the initial rho value (estimate of the first autoregressive parameter) on the RHO subcommand.

Iterations. You can specify the maximum number of iterations the procedure is allowed to cycle through in calculating estimates on the MXITER subcommand.

Statistical Output. To display estimates and statistics at each iteration in addition to the default output, specify TSET PRINT=DETAILED before AREG. To display only the final parameter estimates, use TSET PRINT=BRIEF (see TSET for more information).

New Variables. To evaluate the regression summary table without creating new variables, specify TSET NEWVAR=NONE prior to AREG. This can result in faster processing time. To add new variables without erasing the values of previous Forecasting-generated variables, specify TSET NEWVAR=ALL. This saves all new variables generated during the session to the active dataset and may require extra processing time.

Basic Specification

The basic specification is one dependent series name, the keyword WITH, and one or more independent series names.

• By default, procedure AREG estimates a regression model using the Prais-Winsten (GLS) technique. The number of iterations is determined by the convergence value set on TSET CNVERGE (default of 0.001), up to the default maximum number of 10 iterations. A 95% confidence interval is used unless it is changed by a TSET CIN command prior to the AREG procedure.
• Unless the default on TSET NEWVAR is changed prior to AREG, five variables are automatically created, labeled, and added to the active dataset: fitted values (FIT#1), residuals (ERR#1), lower confidence limits (LCL#1), upper confidence limits (UCL#1), and standard errors of prediction (SEP#1).

Subcommand Order

• VARIABLES must be specified first.
• The remaining subcommands can be specified in any order.

Syntax Rules

• VARIABLES can be specified only once.
• Other subcommands can be specified more than once, but only the last specification of each one is executed.

Operations

• AREG cannot forecast beyond the end of the regressor (independent) series (see PREDICT for more information).
• Method ML allows missing data anywhere in the series. Missing values at the beginning and end are skipped and the analysis proceeds with the first nonmissing case using Melard’s algorithm. If imbedded missing values are found, they are noted and the Kalman filter is used for estimation.
• Methods PW and CO allow missing values at the beginning or end of the series but not within the series. Missing values at the beginning or end of the series are skipped. If imbedded missing values are found, a warning is issued suggesting the ML method be used instead and the analysis terminates. (See RMV for information on replacing missing values.)
• Series with missing cases may require extra processing time.

Limitations

• Maximum 1 VARIABLES subcommand.
• Maximum 1 dependent series in the series list. There is no limit on the number of independent series.