The HPF Procedure

Smoothing Model Specification Options for IDM Statement

The smoothing model options describe how to forecast the demand interval, size, and average demand components (INTERVAL= option, SIZE= option, and AVERAGE= option).

If the smoothing model options are not specified, the following are the defaults for the demand interval, size, and average components:

interval=(transform=auto method=bestn
          levelrest=(0.0001 0.9999)
          trendrest=(0.0001 0.9999)
          damprest =(0.0001 0.9999) criterion=rmse bounds=(1,.));

size    =(transform=auto method=bestn
          levelrest=(0.0001 0.9999)
          trendrest=(0.0001 0.9999)
          damprest =(0.0001 0.9999) criterion=rmse);

average  =(transform=auto method=bestn
          levelrest=(0.0001 0.9999)
          trendrest=(0.0001 0.9999)
          damprest =(0.0001 0.9999) criterion=rmse);

The preceding smoothing model options provide the typical automation in intermittent demand model selection.

The following smoothing model options can be specified:

BOUNDS=(number, number)

specifies the component forecast bound. See the section IDM Smoothing Model Forecast Bounds Options.

CRITERION=option SELECT=option

specifies the model selection criterion (statistic of fit) to be used to select from several candidate models. This option is often used in conjunction with the HOLDOUT= option specified in the FORECAST statement. The CRITERION= option can also be specified as SELECT=. The default is CRITERION=RMSE. The statistics of fit provided are the same as those provided in the FORECAST statement.

DAMPPARM=number

specifies the damping weight parameter initial value. See the section IDM Smoothing Model Forecast Bounds Options.

DAMPREST=(number, number)

specifies the damping weight parameter restrictions. See the section IDM Smoothing Model Forecast Bounds Options.

LEVELPARM=number

specifies the level weight parameter initial value. See the section IDM Smoothing Model Forecast Bounds Options.

LEVELREST=(number, number)

specifies the level weight parameter restrictions. See the section IDM Smoothing Model Forecast Bounds Options.

MEDIAN

specifies that the median forecast values are to be estimated. Forecasts can be based on the mean or median. By default the mean value is provided. If no transformation is applied to the actual series by using the TRANSFORM= option, the mean and median component forecast values are identical.

METHOD=method-name

specifies the forecasting model to be used to forecast the demand component. A single model can be specified, or a group of candidate models can be specified. If a group of models is specified, the model used to forecast the accumulated time series is selected based on the CRITERION= option of the IDM statement and the HOLDOUT= option of the FORECAST statement. The default is METHOD=BESTN. The following forecasting models are provided:

SIMPLE: simple (single) exponential smoothing
DOUBLE: double (Brown) exponential smoothing
LINEAR: linear (Holt) exponential smoothing
DAMPTREND: damped trend exponential smoothing
BESTN: best candidate nonseasonal smoothing model (SIMPLE, DOUBLE, LINEAR, DAMPTREND)

NOEST

specifies that the smoothing model parameters are fixed values. To use this option, all of the smoothing model parameters must be explicitly specified. By default, the smoothing model parameters are optimized.

NOSTABLE

specifies that the smoothing model parameters are not restricted to the additive invertible region of the parameter space. By default, the smoothing model parameters are restricted to be inside the additive invertible region of the parameter space.

TRANSFORM=option

specifies the time series transformation to be applied to the demand component. The following transformations are provided:

NONE: no transformation
LOG: logarithmic transformation
SQRT: square-root transformation
LOGISTIC: logistic transformation
BOXCOX(n): Box-Cox transformation with parameter number n, where n is between –5 and 5
AUTO: automatically choose between NONE and LOG based on model selection criteria. This option is the default.

When the TRANSFORM= option is specified, the demand component must be strictly positive. After the demand component is transformed, the model parameters are estimated by using the transformed component. The forecasts of the transformed component are then computed, and finally the transformed component forecasts are inverse transformed. The inverse transform produces either mean or median forecasts depending on whether the MEDIAN option is specified.

TRENDPARM=number

specifies the trend weight parameter initial value. See the section Smoothing Model Parameter Specification Options.

TRENDREST=(number, number)

specifies the trend weight parameter restrictions. See the section Smoothing Model Parameter Specification Options.

Last updated: March 05, 2026