The ESM Procedure

specifies how the data set observations are accumulated within each time period for the variables listed in the FORECAST statement. If the ACCUMULATE= option is not specified in the FORECAST statement, accumulation is determined by the ACCUMULATE= option of the ID statement. Use the ACCUMULATE= option with multiple FORECAST statements when you want different accumulation specifications for different variables. See the ID statement ACCUMULATE= option for more details.

specifies the significance level to use in computing the confidence limits of the forecast. The ALPHA= value must be between 0 and 1. The default is ALPHA=0.05, which produces 95% confidence intervals.

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 time series by using the TRANSFORM= option, the mean and median forecast values are identical.

specifies the forecasting model to be used to forecast the time series. The default is MODEL=SIMPLE, which performs simple exponential smoothing. The following forecasting models are provided:

NONE

no forecast

SIMPLE

simple (single) exponential smoothing. This is the default.

DOUBLE

double (Brown) exponential smoothing

LINEAR

linear (Holt) exponential smoothing

DAMPTREND

damped trend exponential smoothing

ADDSEASONAL|SEASONAL

additive seasonal exponential smoothing

MULTSEASONAL

multiplicative seasonal exponential smoothing

WINTERS

Winters multiplicative method

ADDWINTERS

Winters additive method

When the option MODEL=NONE is specified, the time series is appended with missing values in the OUT= data set. This option is useful when the results stored in the OUT= data set are used in a subsequent analysis where forecasts of the independent variables are needed to forecast the dependent variable.

specifies the number of observations used to initialize the backcast states. The default is the entire series.

specifies that actual values excluded by the BACK= option are replaced with one-step-ahead forecasts in the OUT= data set.

specifies that embedded missing values are replaced with one-step-ahead forecasts in the OUT= data set.

specifies how missing values (either input or accumulated) are assigned in the accumulated time series for variables listed in the FORECAST statement. If the SETMISSING= option is not specified in the FORECAST statement, missing values are set based on the SETMISSING= option of the ID statement. See the ID statement SETMISSING= option for more details.

specifies the time series transformation to be applied to the input or accumulated time series. The following transformations are provided:

NONE

no transformation. This is the default.

LOG

logarithmic transformation

SQRT

square-root transformation

LOGISTIC

logistic transformation

BOXCOX(n)

Box-Cox transformation with parameter number where number is between –5 and 5

When the TRANSFORM= option is specified, the time series must be strictly positive. After the time series is transformed, the model parameters are estimated by using the transformed series. The forecasts of the transformed series are then computed, and finally the transformed series forecasts are inverse transformed. The inverse transform produces either mean or median forecasts depending on whether the MEDIAN option is specified. The sections Transformations and Inverse Transformations describe this in more detail.

specifies which forecast values are appended to the actual values in the OUT= and OUTSUM= data sets. The following USE= options are provided:

PREDICT

The predicted values are appended to the actual values. This option is the default.

LOWER

The lower confidence limit values are appended to the actual values.

UPPER

The upper confidence limit values are appended to the actual values.

Thus, the USE= option enables the OUT= and OUTSUM= data sets to be used for worst-case, best-case, average-case, and median-case decisions.

specifies how beginning or ending zero values (either input or accumulated) are interpreted in the accumulated time series for variables listed in the FORECAST statement. If the ZEROMISS= option is not specified in the FORECAST statement, beginning or ending zero values are set to missing values based on the ZEROMISS= option of the ID statement. See the ID statement ZEROMISS= option for more details.