The X13 Procedure

ESTIMATE Statement

ESTIMATE options;

The ESTIMATE statement estimates the regARIMA model. The regARIMA model is specified by the REGRESSION, INPUT, EVENT, and ARIMA statements or by the MDLINFOIN= data set in the PROC X13 statement. Estimation output includes point estimates and standard errors for all estimated AR, MA, and regression parameters; the maximum likelihood estimate of the variance $\sigma ^2$ ; t statistics for individual regression parameters; $\chi ^2$ statistics for assessing the joint significance of the parameters associated with certain regression effects (if included in the model); and likelihood-based model selection statistics (if the exact likelihood function is used). The regression effects for which $\chi ^2$ statistics are produced are fixed seasonal effects.

Tables displayed in the output associated with estimation are "Exact ARMA Likelihood Estimation Iteration Tolerances," "Average Absolute Percentage Error in within-Sample Forecasts," "ARMA Iteration History," "AR/MA Roots," "Exact ARMA Likelihood Estimation Iteration Summary," "Regression Model Parameter Estimates," "Chi-Squared Tests for Groups of Regressors," "Exact ARMA Maximum Likelihood Estimation," and "Estimation Summary."

The following options can appear in the ESTIMATE statement:

EXACT=ARMA | MA | NONE

specifies the likelihood function for estimation, likelihood evaluation, and forecasting. You can specify the following values:

ARMA: uses the likelihood function that is exact for both AR and MA parameters.
MA: uses the likelihood function that is exact for MA parameters, but conditional for AR parameters.
NONE: uses the likelihood function that is conditional for both AR and MA parameters.

The ARMA estimation iterations are displayed in the "Iteration History" table, which is available when the ITPRINT option is specified. By default, EXACT=ARMA.

ITPRINT

displays the "Iteration History" table. This table includes detailed output for estimation iterations, including log-likelihood values, parameters, counts of function evaluations, and iterations. It is useful to examine the "Iteration History" table when errors occur within estimation iterations. By default, only successful iterations are displayed, unless the PRINTERR option is specified. An unsuccessful iteration is an iteration that is restarted due to a problem such as a root inside the unit circle. Successful iterations have a status of 0. If restarted iterations are displayed, a note at the end of the table gives definitions for status codes that indicate a restarted iteration. For restarted iterations, the number of function evaluations and the number of iterations is –1, which is displayed as missing. If regression parameters are included in the model, then both IGLS and ARMA iterations are included in the table. The number of function evaluations is a cumulative total.

MAXITER=value

specifies the maximum number of iterations used in estimating the AR and MA parameters. For models that include regression variables, this limit applies to the total number of ARMA iterations over all iterations of the iterative generalized least squares (IGLS) algorithm. For models without regression variables, value is the maximum number of iterations allowed for the set of ARMA iterations. By default, MAXITER=1500.

PRINTERR

causes restarted iterations to be included in the "Iteration History" table if ITPRINT is specified; creates the "Restarted Iterations" table if ITPRINT is not specified. Whether or not PRINTERR is specified, a WARNING message is printed to the log file if any iteration is restarted during estimation.

TOL=value

specifies the convergence tolerance for the nonlinear estimation. Absolute changes in the log-likelihood are compared to the TOL= value to check convergence of the estimation iterations. For models with regression variables, the TOL= value is used to check convergence of the IGLS iterations (where the regression parameters are reestimated for each new set of AR and MA parameters). For models without regression variables, there are no IGLS iterations, and the TOL= value is then used to check convergence of the nonlinear iterations that are used to estimate the AR and MA parameters. The default value is TOL=0.00001. The minimum tolerance value is a positive value based on the machine precision and the length of the series. If a tolerance less than the minimum supported value is specified, an error message is displayed and the series is not processed.