The VARMAX Procedure

GARCH Statement

GARCH options ;

The GARCH statement specifies a GARCH-type multivariate conditional heteroscedasticity model.

The following options can be used in the GARCH statement.

FORM=value

specifies the representation for a GARCH model. Valid values are as follows:

BEKK: specifies a BEKK representation. This is the default.
CCC: specifies a constant conditional correlation representation.

OUTHT=SAS-data-set

writes the conditional covariance matrix to an output data set.

P=number P=(number-list)

specifies the order of the process or the subset of GARCH terms to be fitted. For example, you can specify the P=(1,3) option. The P=3 option is equivalent to the P=(1,2,3) option. The default is P=0.

Q=number Q=(number-list)

specifies the order of the process or the subset of ARCH terms to be fitted. This option is required in the GARCH statement. For example, you can specify the Q=(2) option. The Q=2 option is equivalent to the Q=(1,2) option.

For the VAR(1)–ARCH(1) model,

   model y1 y2 / p=1;
   garch q=1 form=bekk;

For the multivariate GARCH(1,1) model,

   model y1 y2;
   garch q=1 p=1 form=ccc;

Other multivariate GARCH-type models are

   model y1 y2 = x1 / xlag=1;
   garch q=1;

   model y1 y2 / q=1;
   garch q=1 p=1;

See the section Multivariate GARCH Modeling for details.