The UCM Procedure

LEVEL Statement

LEVEL <options> ;

The LEVEL statement is used to include a level component in the model. The level component, either by itself or together with a slope component (see the SLOPE statement), forms the trend component, $\text{[math]}$ , of the model. If the slope component is absent, the resulting trend is a random walk (RW) specified by the following equations:

$\text{[math]}$

If the slope component is present, signified by the presence of a SLOPE statement, a locally linear trend (LLT) is obtained. The equations of LLT are as follows:

	$\text{[math]}$	$\text{[math]}$	$\text{[math]}$
	$\text{[math]}$	$\text{[math]}$	$\text{[math]}$

In either case, the options in the LEVEL statement are used to specify the value of $\text{[math]}$ and to request forecasts of $\text{[math]}$ . The SLOPE statement is used for similar purposes in the case of slope $\text{[math]}$ . The following examples illustrate the use of the LEVEL statement. Assuming that a SLOPE statement is not added subsequently, a simple random walk trend is specified by the following statement:

      level;

The following statements specify a locally linear trend with value of $\text{[math]}$ fixed at 4. It also requests printing of filtered values of $\text{[math]}$ . The value of $\text{[math]}$ , the disturbance variance in the slope equation, is estimated from the data.

      level variance=4 noest print=filter;
      slope;

CHECKBREAK: turns on the checking of breaks in the level component.
NOEST: fixes the value of $\text{[math]}$ to the value specified in the VARIANCE= option.
PLOT=FILTER
PLOT=SMOOTH
PLOT=( <FILTER> <SMOOTH> ): requests plotting of the filtered or smoothed estimate of the level component.
PRINT=FILTER
PRINT=SMOOTH
PRINT=( <FILTER> <SMOOTH> ): requests printing of the filtered or smoothed estimate of the level component.
VARIANCE=value: specifies an initial value for $\text{[math]}$ , the disturbance variance in the $\text{[math]}$ equation at the start of the parameter estimation process. Any nonnegative value, including zero, is an acceptable starting value.