The VARMAX Procedure

The TEST statement performs the Wald test for the joint linear hypothesis that is specified in the statement. Each restriction specifies a linear hypothesis to be tested. If you specify more than one restriction, separate them with commas. Specify the restrictions in the same manner as in the RESTRICT statement. For information about how to define restriction by using matrix expressions, operators, and functions, see the section RESTRICT Statement. You can specify any number of TEST statements.

To use the TEST statement, you need to know the form of the model. If you do not specify the GARCH statement, the COINTEG statement, or the ECM=, P=, Q=, or XLAG= option in the MODEL statement, then the TEST statement is not applicable. Nonlinear restrictions on parameters are not supported.

For information about the Wald test, see the section Granger Causality Test.

The following is an example of the TEST statement for a bivariate (k=2) VAR(2) model:

proc varmax data=one;
   model y1 y2 / p=2;
   test AR(1,1,2) = 0, AR(2,1,2) = 0;
run;

After estimating the parameters, the TEST statement tests the null hypothesis that AR(1,1,2)=0 and AR(2,1,2)=0. Like the RESTRICT statement, the preceding TEST statement can be abbreviated as follows:

test AR(1,1,2) = AR(2,1,2) = 0;

or

test AR(1,1,2), AR(2,1,2);

Note that the following statements are different from the preceding statement:

test AR(1,1,2);
test AR(2,1,2);

These two TEST statements are to test two null hypotheses separately: one is AR(1,1,2)=0, and the other is AR(2,1,2)=0.

For the vector error correction models, you can test the hypothesis on the AR(1,.,.) parameters (that is, ) by using the TEST statement, because asymptotically these parameters follow a normal distribution and the Wald test can be applied. For the same reason, you can use the CONST(.) or LTREND(.) function in the TEST statement if the ECTREND option in the COINTEG statement is specified. However, the BETA(.,.), ECCONST(.), and ECLTREND(.) functions are not supported in the TEST statement. For example, the following statements are supported,

model y1-y4 / p=2;
cointeg rank=1 ectrend;
test AR(1,1,1);
test CONST(2);

However, the following statements are not supported,

model y1-y4 / p=2;
cointeg rank=1 ectrend;
test BETA(1,1) = BETA(2,1) = 0;

or

model y1-y4 / p=2;
cointeg rank=1 ectrend;
test ECCONST(1) = 0.2;