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, , of the model. If the slope component is absent, the resulting trend is a random walk (RW) specified by the following equations:
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:
In either case, the options in the LEVEL statement are used to specify the value of and to request forecasts of . The SLOPE statement is used for similar purposes in the case of slope . 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 fixed at 4. It also requests printing of filtered values of . The value of , the disturbance variance in the slope equation, is estimated from the data.
level variance=4 noest print=filter; slope;