The ESM Procedure
The ESM procedure can create the OUT=, OUTEST=, OUTFOR=, OUTSTAT=, and OUTSUM= data sets. These data sets contain the variables listed in the BY statement and statistics related to the variables listing in the FORECAST statement. In general, if a forecasting step related to an output data set fails, the values of this step are not recorded or are set to missing in the related output data set and appropriate error and/or warning messages are recorded in the log.
The OUT= data set contains the variables specified in the BY, ID, and FORECAST statements. If the ID statement is specified, the ID variable values are aligned and extended based on the ALIGN= and INTERVAL= options. The values of the variables specified in the FORECAST statements are accumulated based on the ACCUMULATE= option, and missing values are interpreted based on the SETMISSING= option. If the REPLACEMISSING option is specified, embedded missing values are replaced by the one-step-ahead predicted values.
These FORECAST variables are then extrapolated based on the forecasts from the fitted models, or extended with missing values when the MODEL=NONE option is specified. If USE=LOWER is specified, the variable is extrapolated with the lower confidence limits; if USE=UPPER, the variable is extrapolated using the upper confidence limits; otherwise, the variable values are extrapolated with the predicted values. If the TRANSFORM= option is specified, the predicted values contain either mean or median forecasts depending on whether or not the MEDIAN option is specified.
If any of the forecasting steps fail for a particular variable, the variable is extended by missing values.
The OUTEST= data set contains the variables specified in the BY statement as well as the variables listed below. For variables listed in FORECAST statements where the option MODEL=NONE is specified, no observations are recorded in the OUTEST= data set. For variables listed in FORECAST statements where the option MODEL=NONE is not specified, the following variables in the OUTEST= data set contain observations related to the parameter estimation step:
- _NAME_
-
variable name
- _MODEL_
-
forecasting model
- _TRANSFORM_
-
transformation
- _PARM_
-
parameter name
- _EST_
-
parameter estimate
- _STDERR_
-
standard errors
- _TVALUE_
-
t values
- _PVALUE_
-
probability values
If the parameter estimation step fails for a particular variable, no observations are output to the OUTEST= data set for that variable.
The OUTFOR= data set contains the variables specified in the BY statement as well as the variables listed below. For variables listed in FORECAST statements where the option MODEL=NONE is specified, no observations are recorded in the OUTFOR= data set for these variables. For variables listed in FORECAST statements where the option MODEL=NONE is not specified, the following variables in the OUTFOR= data set contain observations related to the forecasting step:
- _NAME_
-
variable name
- _TIMEID_
-
time ID values
- ACTUAL
-
actual values
- PREDICT
-
predicted values
- STD
-
prediction standard errors
- LOWER
-
lower confidence limits
- UPPER
-
upper confidence limits
- ERROR
-
prediction errors
If the forecasting step fails for a particular variable, no observations are recorded in the OUTFOR= data set for that variable. If the TRANSFORM= option is specified, the values in the preceding variables are the inverse transform forecasts. If the MEDIAN option is specified, the median forecasts are stored; otherwise, the mean forecasts are stored.
The OUTPROCINFO= data set contains information about the run of the ESM procedure. The following variables are present:
- _SOURCE_
-
set to the name of the procedure, in this case ESM
- _NAME_
-
name of an item being reported; can be the number of errors, notes, or warnings, number of forecasts requested, and so on
- _LABEL_
-
descriptive label for the item in _NAME_
- _STAGE_
-
set to the current stage of the procedure, for ESM this is set to ALL
- _VALUE_
-
value of the item specified in _NAME_
The OUTSTAT= data set contains the variables specified in the BY statement as well as the variables listed below. For variables listed in FORECAST statements where the option MODEL=NONE is specified, no observations are recorded for these variables in the OUTSTAT= data set. For variables listed in FORECAST statements where the option MODEL=NONE is not specified, the following variables in the OUTSTAT= data set contain observations related to the statistics of fit:
- _NAME_
-
variable name
- _REGION_
-
the region in which the statistics are calculated. Statistics calculated in the fit region are indicated by FIT. Statistics calculated in the forecast region, which happens only if the BACK= option is greater than zero, are indicated by FORECAST.
- DFE
-
degrees of freedom error
- N
-
number of observations
- NOBS
-
number of observations used
- NMISSA
-
number of missing actuals
- NMISSP
-
number of missing predicted values
- NPARMS
-
number of parameters
- TSS
-
total sum of squares
- SST
-
corrected total sum of squares
- SSE
-
sum of square error
- MSE
-
mean square error
- UMSE
-
unbiased mean square error
- RMSE
-
root mean square error
- URMSE
-
unbiased root mean square error
- MAPE
-
mean absolute percent error
- MAE
-
mean absolute error
- MASE
-
mean absolute scaled error
- RSQUARE
-
R square
- ADJRSQ
-
adjusted R square
- AADJRSQ
-
Amemiya’s adjusted R square
- RWRSQ
-
random walk R square
- AIC
-
Akaike information criterion
- AICC
-
finite sample corrected AIC
- SBC
-
Schwarz Bayesian information criterion
- APC
-
Amemiya’s prediction criterion
- MAXERR
-
maximum error
- MINERR
-
minimum error
- MINPE
-
minimum percent error
- MAXPE
-
maximum percent error
- ME
-
mean error
- MPE
-
mean percent error
- MDAPE
-
median absolute percent error
- GMAPE
-
geometric mean absolute percent error
- MINPPE
-
minimum predictive percent error
- MAXPPE
-
maximum predictive percent error
- MSPPE
-
mean predictive percent error
- MAPPE
-
symmetric mean absolute predictive percent error
- MDAPPE
-
median absolute predictive percent error
- GMAPPE
-
geometric mean absolute predictive percent error
- MINSPE
-
minimum symmetric percent error
- MAXSPE
-
maximum symmetric percent error
- MSPE
-
mean symmetric percent error
- SMAPE
-
symmetric mean absolute percent error
- MDASPE
-
median absolute symmetric percent error
- GMASPE
-
geometric mean absolute symmetric percent error
- MINRE
-
minimum relative error
- MAXRE
-
maximum relative error
- MRE
-
mean relative error
- MRAE
-
mean relative absolute error
- MDRAE
-
median relative absolute error
- GMRAE
-
geometric mean relative absolute error
- MINAPES
-
minimum absolute error percent of standard deviation
- MAXAPES
-
maximum absolute error percent of standard deviation
- MAPES
-
mean absolute error percent of standard deviation
- MDAPES
-
median absolute error percent of standard deviation
- GMAPES
-
geometric mean absolute error percent of standard deviation
If the statistics of fit cannot be computed for a particular variable, no observations are recorded in the OUTSTAT= data set for that variable. If the TRANSFORM= option is specified, the values in the preceding variables are computed based on the inverse transform forecasts. If the MEDIAN option is specified, the median forecasts are the basis; otherwise, the mean forecasts are the basis.
See Chapter 53: Forecasting Process Details, for more information about the calculation of forecasting statistics of fit.
The OUTSUM= data set contains the variables specified in the BY statement as well as the variables listed below. The OUTSUM= data set records the summary statistics for each variable specified in a FORECAST statement. For variables listed in FORECAST statements where the option MODEL=NONE is specified, the values related to forecasts are set to missing for those variables in the OUTSUM= data set. For variables listed in FORECAST statements where the option MODEL=NONE is not specified, the forecast values are set based on the USE= option.
The following variables related to summary statistics are based on the ACCUMULATE= and SETMISSING= options:
- _NAME_
-
variable name
- _STATUS_
-
forecasting status. Nonzero values imply that no forecast was generated for the series.
- NOBS
-
number of observations
- N
-
number of nonmissing observations
- NMISS
-
number of missing observations
- MIN
-
minimum value
- MAX
-
maximum value
- MEAN
-
mean value
- STDDEV
-
standard deviation
The following variables related to forecast summation are based on the LEAD= and STARTSUM= options:
- PREDICT
-
forecast summation predicted values
- STD
-
forecast summation prediction standard errors
- LOWER
-
forecast summation lower confidence limits
- UPPER
-
forecast summation upper confidence limits
Variance-related computations are computed only when no transformation is specified (TRANSFORM=NONE).
The following variables related to multistep forecast are based on the LEAD= and USE= options:
- _LEADn_
-
multistep forecast (n ranges from one to the value of the LEAD= option). If USE=LOWER, this variable contains the lower confidence limits; if USE=UPPER, this variable contains the upper confidence limits; otherwise, this variable contains the predicted values.
If the forecast step fails for a particular variable, the variables that are related to forecasting are set to missing for that variable. The OUTSUM= data set contains both a summary of the (accumulated) time series and optionally its forecasts for all series.