The HPFUCMSPEC Procedure

SLOPE Statement

SLOPE <options>;

The SLOPE statement is used to include a slope component in the model. The slope component cannot be used without the level component. The level and slope specifications jointly define the trend component of the model. A SLOPE statement without the accompanying LEVEL statement is ignored. The equations of the trend, defined jointly by the level and slope , are as follows:

StartLayout 1st Row 1st Column mu Subscript t 2nd Column equals 3rd Column mu Subscript t minus 1 Baseline plus beta Subscript t minus 1 Baseline plus eta Subscript t Baseline comma eta Subscript t Baseline tilde i period i period d period upper N left-parenthesis 0 comma sigma Subscript eta Superscript 2 Baseline right-parenthesis 2nd Row 1st Column beta Subscript t 2nd Column equals 3rd Column beta Subscript t minus 1 Baseline plus xi Subscript t Baseline comma xi Subscript t Baseline tilde i period i period d period upper N left-parenthesis 0 comma sigma Subscript xi Superscript 2 Baseline right-parenthesis EndLayout

The SLOPE statement is used to specify the value of the disturbance variance in the slope equation and to request forecasts of . The following statements request that a locally linear trend be used in the model. The disturbance variances and are estimated from the data.

level;
slope;

You can request a locally linear trend with fixed slope using the following statements:

level;
slope variance=0 noest;

The following options can be specified in the SLOPE statement.

NOEST: fixes the value of the disturbance variance to the value specified in the VARIANCE= option.
VARIANCE=value: supplies an initial value for the disturbance variance in the equation, at the start of the parameter estimation process. Any nonnegative value, including zero, is an acceptable starting value.

Last updated: March 05, 2026