The ESM Procedure |

Data Set Output |

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 46, 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:

- _LEAD_
multistep forecast ( 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.

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