UCM Procedure
Modeling Regression Effects
A predictor variable can affect the response variable in a variety of ways. The UCM procedure enables you to model several different types of predictor-response relationships:
The predictor-response relationship is linear, and the regression coefficient does not change with time. This is the simplest kind of relationship and such predictors are specified in the MODEL statement.
The predictor-response relationship is linear, but the regression coefficient does change with time. Such predictors are specified in the RANDOMREG statement. Here the regression coefficient is assumed to evolve as a random walk.
The predictor-response relationship is nonlinear and the relationship can change with time. This type of relationship can be approximated by an appropriate time-varying spline. Such predictors are specified in the SPLINEREG statement.
The response depends on contemporaneous and lagged values of the predictor. This type of relationship is called transfer-function relationship, which can be specified in the TF statement.
A response variable can depend on its own past values—that is, lagged dependent values. Such a relationship can be specified in the DEPLAG statement.