Chapter Contents |
Previous |
Next |

The FORECAST Procedure |

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 -AR
*n* - 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 -AR
*n*. 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*j*th season of the*i*th 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 R
^{2}statistic,*R*=1-^{2}*SSE*/*SST*. If the model fits the series badly, the model error sum of squares*SSE*may be larger than*SST*and the R^{2}statistic will be negative. - ADJRSQ
- The observation contains the adjusted R
^{2}statistic.*ADJRSQ*= 1 - ([(*n*-1)/(*n*-*k*)]) (1-*R*) .^{2} - ARSQ
- The observation contains Amemiya's adjusted R
^{2}statistic.*ARSQ*= 1-([(*n*+*k*)/(*n*-*k*)]) (1-*R*) .^{2} - RW_RSQ
- The observation contains the random walk R
^{2}statistic (Harvey's*R*_{D}^{2}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-*R*) = ([(^{2}*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.

Chapter Contents |
Previous |
Next |
Top |

Copyright © 1999 by SAS Institute Inc., Cary, NC, USA. All rights reserved.