RESTRICT Statement

The VARMAX Procedure

RESTRICT Statement

RESTRICT restriction ... restriction ;

The RESTRICT statement restricts the specified parameters to the specified values. Only one RESTRICT statement is allowed.

The restriction's form is parameter = value and each restriction is separated by commas. Parameters are referred by the following keywords:

CONST(i), the intercept parameter of the current value ith time series y_it
AR(l,i,j), the autoregressive parameter of the previous lag l value of the jth endogenous (dependent) variable, y_j,t-l, to the ith endogenous variable at time t, y_it
XL(l,i,j), the exogenous parameter of the previous lag l value of the jth exogenous (independent) variable, x_j,t-l, to the ith endogenous variable at time t, y_it
SDUMMY(i,j), the jth seasonal dummy of the ith time series at time t, y_it, where j = 1, ... ,(nseason-1)

To use the RESTRICT statement, you need to know the form of the model. If you do not specify any order of the model, the RESTRICT statement is not applicable.

Restricted parameter estimates are computed by introducing a Lagrangian parameter for each restriction (Pringle and Raynor 1971). The Lagrangian parameter measures the sensitivity of the sum of square errors to the restriction. The estimates of these Lagrangian parameters and their significances are printed in the restriction results table.

The following are examples of the RESTRICT statement. The first example shows a bivariate (k=2) VAR(2) model,

   proc varmax data=one;
      model y1 y2 / p=2;
      restrict AR(1,1,2)=0, AR(2,1,2)=0.3;  
   run;

The following shows a bivariate (k=2) VARX(1,1) model with three exogenous variables,

   proc varmax data=two;
      model y1 = x1 x2, y2 = x2 x3 / p=1 xlag=1;
      restrict XL(0,1,1)=-1.2, XL(1,2,3)=0;  
   run;

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