The VARMAX Procedure

The Bayesian vector autoregressive (BVAR) model avoids problems of collinearity and overparameterization that often occur with the use of VAR models. BVAR models avoid these problems by imposing priors on the AR parameters.

The following statements fit a BVAR(1) model to the simulated data:

/*--- Bayesian Vector Autoregressive Process ---*/

proc varmax data=simul1;
   model y1 y2 / p=1 noint
                 prior=(lambda=0.9 theta=0.1);
run;

The hyperparameters, LAMBDA=0.9 and THETA=0.1, in the PRIOR= option control the prior covariance. Part of the VARMAX procedure output is shown in Figure 42.11, whose parameter estimates are slightly different from those in Figure 42.3. By choosing the appropriate priors, you might be able to obtain more accurate forecasts by using a BVAR model instead of an unconstrained VAR model. For more information, see the section Bayesian VAR and VARX Modeling.