The UCM Procedure

RANDOMREG Statement

RANDOMREG regressors </ options > ;

The RANDOMREG statement is used to specify regressors with time-varying regression coefficients. Each regression coefficient—say, $\beta _{t}$ — is assumed to evolve as a random walk:

$\beta _{t} = \beta _{t-1} + \eta _{t}, \; \; \; \; \eta _ t \; \sim \; i.i.d. \; \; N( 0, \sigma ^{2} )$

Of course, if the random walk disturbance variance $\sigma ^{2}$ is zero, then the regression coefficient is not time varying, and it reduces to the standard regression setting. There can be multiple RANDOMREG statements, and each statement can contain one or more regressors. The regressors in a given RANDOMREG statement form a group that is assumed to share the same disturbance variance parameter. The random walks associated with different regressors are assumed to be independent. For an example of using this statement see Example 34.4. See the section Reporting Parameter Estimates for Random Regressors for additional information about the way parameter estimates are reported for this type of regressors.

NOEST: fixes the value of $\sigma ^{2}$ to the value specified in the VARIANCE= option.
PLOT=FILTER PLOT=SMOOTH PLOT=( <FILTER> <SMOOTH> ): requests plotting of filtered or smoothed estimate of the time-varying regression coefficient.
PRINT=FILTER PRINT=SMOOTH PRINT=( <FILTER> <SMOOTH> ): requests printing of the filtered or smoothed estimate of the time-varying regression coefficient.
VARIANCE=value: specifies an initial value for $\sigma ^{2}$ during the parameter estimation process. Any nonnegative value, including zero, is an acceptable starting value.