The AUTOREG Procedure

The RESTRICT statement provides constrained estimation and places restrictions on the parameter estimates for covariates in the preceding MODEL statement. The AR, GARCH, and HETERO parameters are also supported in the RESTRICT statement. Any number of RESTRICT statements can follow a MODEL statement. Several restrictions can be specified in a single RESTRICT statement by separating the individual restrictions with commas.

Each restriction is written as a linear equation composed of constants and parameter names. Refer to model parameters by the name of the corresponding regressor variable. Each name used in the equation must be a regressor in the preceding MODEL statement. Use the keyword INTERCEPT to refer to the intercept parameter in the model. See the section OUTEST= Data Set for the names of these parameters.

The following is an example of a RESTRICT statement:

model y = a b c d;
restrict a+b=0, 2*d-c=0;

When restricting a linear combination of parameters to be 0, you can omit the equal sign. For example, the following RESTRICT statement is equivalent to the preceding example:

restrict a+b, 2*d-c;

The following RESTRICT statement constrains the parameters estimates for three regressors (X1, X2, and X3) to be equal:

restrict x1 = x2, x2 = x3;

The preceding restriction can be abbreviated as follows:

restrict x1 = x2 = x3;

The following example shows how to specify AR, GARCH, and HETERO parameters in the RESTRICT statement:

model y = a b / nlag=2 garch=(p=2,q=3,mean=sqrt);
hetero c d;
restrict _A_1=0,_AH_2=0.2,_HET_2=1,_DELTA_=0.1;

Only simple linear combinations of parameters can be specified in RESTRICT statement expressions; complex expressions that involve parentheses, division, functions, or complex products are not allowed.