The following features have been added to the VARMAX procedure:
Vector error correction models in ARMA-GARCH form are supported. You can use the COINTEG statement together with the Q= option in the MODEL statement and the GARCH statement to model the cointegration relationship between multiple time series that have GARCH-type innovations.
The linear equality and inequality constraints for any parameters to be estimated in vector error correction models are supported. You can use the BOUND and RESTRICT statement to study the restricted cointegrated systems.
The covariance and standard errors of the parameter estimates of the adjustment coefficient matrix and the covariance matrix of innovations in vector error correction models are supported. The outputs of parameter estimates of the long-run parameters and the error correction trend parameters are also supported.
You can apply the Wald tests, by using the TEST statement, on any parameters in vector correction models except the long-run parameters and the error correction trend parameters.
You can specify initial values, by using the INITIAL statement, for any parameters to be estimated in vector error correction models. If you do so, you must specify the full-rank initial matrices for both the adjustment coefficient matrix and the long-run parameters.
A new estimation method, the conditional maximum likelihood method (CML), is supported. This method is especially suitable for estimating VARMAX models on large samples.
The log likelihoods for all types of models are output. These outputs are especially useful if you need to execute the likelihood ratio (LR) tests.
Definitions have been revised for the information criteria: Akaike’s information criterion (AIC), the corrected Akaike’s information criterion (AICC), the Hannan-Quinn criterion (HQC), and the Schwarz Bayesian criterion (SBC, also referred to as BIC). You can compare more types of models, including all forms of multivariate GARCH models.
The ECTREND option is supported in the COINTEG statement. All options in the ECM= option in the MODEL statement are now supported in the COINTEG statement and the ECM= option becomes obsolete. Starting with SAS/ETS 14.1, it is recommended that you use the COINTEG statement instead of the ECM= option to fit vector error correction models.
A new option, the NLC option, is supported in the COINTEG statement. By using this option, you can explicitly require that the adjustment coefficient matrix and the long-run parameters both be full rank when you numerically maximize the likelihood of a vector error correction model.