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 The FORECAST Procedure

## 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.

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.

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.

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