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 or unconditional correlation matrix in the CCC or DCC GARCH model, respectively. 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 or unconditional correlation matrix for the CCC or DCC GARCH model is output in the CCCCorrConstant
or DCCCorrConstant ODS table, respectively. 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. If you specify the FORM=BEKK
option, the SUBFORM= option is ignored. 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.
If you specify the ECM=(NORMALIZE=) or PRIOR= option in the MODEL statement, or if you specify the EXOGENEITY, H=, J=, or
NORMALIZE= option in the COINTEG statement, the GARCH statement is ignored.
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.
