The ESM Procedure

OUT= Data Set

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.

OUTEST= Data Set

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.

OUTFOR= Data Set

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.

OUTPROCINFO= Data Set

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_

OUTSTAT= Data Set

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 50, Forecasting Process Details, for more information about the calculation of forecasting statistics of fit.

OUTSUM= Data Set

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.