The VARMAX Procedure

GARCH Statement

GARCH options ;

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

You can specify the following options:

CORRCONSTANT=ESTIMATE | EXPECT

specifies how to calculate the constant (unconditional) correlation matrix in the CCC (DCC) GARCH model. If you specify CORRCONSTANT=EXPECT, the constant conditional correlation matrix in the CCC GARCH model or the unconditional correlation matrix in the DCC GARCH model is calculated through the standardized residuals, given the other parameters. After parameter estimates are output, the constant (unconditional) correlation matrix for the CCC (DCC) GARCH model is output in the ODS table CCCCorrConstant (DCCCorrConstant). If you specify CORRCONSTANT=ESTIMATE, the correlation matrix is estimated like all other parameters in the model. By default, CORRCONSTANT=ESTIMATE.

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.
DCC: specifies a dynamic 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. By default, 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.

SUBFORM=value

specifies the type of the univariate GARCH model for each innovation in the CCC or DCC GARCH model. The values of the SUBFORM= option are as follows:

EGARCH: specifies the exponential GARCH, or EGARCH, model.
GARCH: specifies the GARCH model with no constraints.
GJR | TGARCH: specifies the GJR GARCH (also called threshold GARCH, or TGARCH) model.
PGARCH: specifies the power GARCH, or PGARCH, model.
QGARCH: specifies the quadratic GARCH, or QGARCH, model.

By default, SUBFORM=GARCH.

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;

For more information, see the section Multivariate GARCH Modeling.