The VARMAX Procedure

The INITIAL statement sets up the initial parameter values for nonlinear optimization when the maximum likelihood method is applied to the estimation of VARMAX or VARMAX-GARCH models. Only one INITIAL statement is allowed. If you specify more than one equation, separate them with commas. The initial parameter values are the solution of the specified linear equations. The equations are specified in the same manner as the restrictions in the RESTRICT statement. For information about how to define equations by using matrix expressions, operators, and functions, see the section RESTRICT Statement.

To use the INITIAL statement, you need to know the form of the model. If you do not specify the P=, Q=, or XLAG= option or the GARCH statement, then the INITIAL statement is not applicable. If you specify the PRIOR=, ECM=, or METHOD=LS option or the COINTEG statement, the INITIAL statement is ignored. Nonlinear equations on parameters are not supported.

The following is an example of the INITIAL statement for a bivariate (k=2) zero-mean VARMA(1,1) model, which is by default estimated by maximum likelihood method because the MA term is present:

proc varmax data=one;
   model y1 y2 / noint p=1 q=1;
   initial AR = 0, MA = 0,
           COV={1 0.5, 0.5 4};
run;

Like the RESTRICT statement, the preceding INITIAL statement can be abbreviated as follows:

initial AR = MA = 0,
        COV={1 0.5, 0.5 4};

or

initial AR, MA, COV={1 0.5, 0.5 4};