OUTEST= Data Set
The FORECAST procedure writes the parameter estimates
and goodness-of-fit statistics to an output data set
when the OUTEST= option is specified.
The OUTEST= data set contains the following variables:
- the BY variables
- the first ID variable, which contains the value of the
ID variable for the last observation in the input data set
used to fit the model
- _TYPE_, a character variable
that identifies the type of each observation
- the VAR statement variables,
which contain statistics and parameter estimates for the input series.
The values contained in the VAR statement variables
depend on the _TYPE_ variable value for the observation.
The observations contained in the OUTEST= data set
are identified by the _TYPE_ variable.
The OUTEST= data set may contain observations with
the following _TYPE_ values:
- AR1 -ARn
- The observation contains estimates of the autoregressive parameters
for the series.
Two-digit lag numbers are used if the value of the NLAGS= option is 10 or more;
in that case these _TYPE_ values are AR01 -ARn.
These observations are output for the STEPAR method only.
- CONSTANT
- The observation contains the estimate of the constant or intercept parameter
for the time-trend model for the series.
For the exponential smoothing and the Winters' methods,
the trend model is centered (that is, t=0)
at the last observation used for the fit.
- LINEAR
- The observation contains the estimate of the linear or slope parameter
for the time-trend model for the series.
This observation is output only if you specify TREND=2 or TREND=3.
- N
- The observation contains the number of nonmissing observations used
to fit the model for the series.
- QUAD
- The observation contains the estimate of the quadratic parameter for the
time-trend model for the series.
This observation is output only if you specify TREND=3.
- SIGMA
- The observation contains the estimate
of the standard deviation of the error term for the series.
- S1 -S3
- The observations contain exponentially smoothed values at
the last observation.
_TYPE_=S1 is the final smoothed value of the single exponential smooth.
_TYPE_=S2 is the final smoothed value of the double exponential smooth.
_TYPE_=S3 is the final smoothed value of the triple exponential smooth.
These observations are output for METHOD=EXPO only.
- S_name
- The observation contains estimates of the seasonal parameters.
For example, if SEASONS=MONTH, the OUTEST= data set will contain
observations with _TYPE_=S_JAN, _TYPE_=S_FEB, _TYPE_=S_MAR,
and so forth.
For multiple-period seasons, the names of the first and last interval
of the season are concatenated to form the season name.
Thus, for SEASONS=MONTH4, the OUTEST= data set will contain observations
with _TYPE_=S_JANAPR, _TYPE_=S_MAYAUG, and _TYPE_=S_SEPDEC.
When the SEASONS= option specifies numbers,
the seasonal factors are labeled _TYPE_=S_i_j.
For example, SEASONS=(2 3) produces observations with _TYPE_ values of
S_1_1, S_1_2, S_2_1, S_2_2, and S_2_3.
The observation with _TYPE_=S_i_j contains the
seasonal parameters for the jth season of the ith seasonal cycle.
These observations are output only for METHOD=WINTERS or METHOD=ADDWINTERS.
- WEIGHT
- The observation contains the smoothing weight used for
exponential smoothing. This is the value of the WEIGHT= option.
This observation is output for METHOD=EXPO only.
- WEIGHT1
- WEIGHT2
- WEIGHT3
- The observations contain the weights used for smoothing
the WINTERS or ADDWINTERS method parameters
(specified by the WEIGHT= option).
_TYPE_=WEIGHT1 is the weight used to smooth the CONSTANT parameter.
_TYPE_=WEIGHT2 is the weight used to smooth the LINEAR and QUAD parameters.
_TYPE_=WEIGHT3 is the weight used to smooth the seasonal parameters.
These observations are output only for the WINTERS and ADDWINTERS methods.
- NRESID
- The observation contains the number of nonmissing residuals, n, used to
compute the goodness-of-fit statistics.
The residuals are obtained by subtracting the
one-step-ahead predicted values from the observed values.
- SST
- The observation contains the total sum of squares for the series,
corrected for the mean.
,
where is the series mean.
- SSE
- The observation contains the sum of the squared residuals,
uncorrected for the mean.
,
where is the one-step predicted value for the series.
- MSE
- The observation contains the mean squared error,
calculated from one-step-ahead forecasts.
MSE = [1/(n-k)] SSE,
where k is the number of parameters in the model.
- RMSE
- The observation contains the root mean square error.
.
- MAPE
- The observation contains the mean absolute percent error.
.
- MPE
- The observation contains the mean percent error.
.
- MAE
- The observation contains the mean absolute error.
.
- ME
- The observation contains the mean error.
.
- MAXE
- The observation contains the maximum error
(the largest residual).
- MINE
- The observation contains the minimum error
(the smallest residual).
- MAXPE
- The observation contains the maximum percent error.
- MINPE
- The observation contains the minimum percent error.
- RSQUARE
- The observation contains the R2 statistic,
R2=1-SSE / SST.
If the model fits the series badly, the model error sum of squares
SSE may be larger than SST and
the R2 statistic will be negative.
- ADJRSQ
- The observation contains the adjusted R2 statistic.
ADJRSQ = 1 - ([(n-1)/(n-k)]) (1- R2) .
- ARSQ
- The observation contains Amemiya's adjusted R2 statistic.
ARSQ = 1-([(n+k)/(n-k)]) (1- R2) .
- RW_RSQ
- The observation contains the random walk R2 statistic
(Harvey's RD2 statistic using
the random walk model for comparison).
RW_RSQ = 1 - ([(n-1)/n]) SSE / RWSSE,
where
,
and
.
- AIC
- The observation contains Akaike's information criterion.
AIC = n ln( SSE / n ) + 2 k.
- SBC
- The observation contains Schwarz's Bayesian criterion.
SBC = n ln( SSE / n ) + k ln( n ).
- APC
- The observation contains Amemiya's prediction criterion.
APC = [1/n] SST ([(n+k)/(n-k)]) (1- R2) = ([(n+k)/(n-k )]) [1/n] SSE.
- CORR
- The observation contains the correlation coefficient between
the actual values and the one-step-ahead predicted values.
- THEILU
- The observation contains Theil's U statistic using original units.
Refer to Maddala (1977, pp. 344-345),
and Pindyck and Rubinfeld (1981, pp. 364-365)
for more information on Theil statistics.
- RTHEILU
- The observation contains Theil's U statistic calculated using relative changes.
- THEILUM
- The observation contains the bias proportion of Theil's U statistic.
- THEILUS
- The observation contains the variance proportion of Theil's U statistic.
- THEILUC
- The observation contains the covariance proportion of Theil's U statistic.
- THEILUR
- The observation contains the regression proportion of Theil's U statistic.
- THEILUD
- The observation contains the disturbance proportion of Theil's U statistic.
- RTHEILUM
- The observation contains the bias proportion of Theil's U statistic,
calculated using relative changes.
- RTHEILUS
- The observation contains the variance proportion of Theil's U statistic,
calculated using relative changes.
- RTHEILUC
- The observation contains the covariance proportion of Theil's U statistic,
calculated using relative changes.
- RTHEILUR
- The observation contains the regression proportion of Theil's U statistic,
calculated using relative changes.
- RTHEILUD
- The observation contains the disturbance proportion of Theil's U statistic,
calculated using relative changes.
Copyright © 1999 by SAS Institute Inc., Cary, NC, USA. All rights reserved.