Output
The following display
shows the results for the two FORECAST statements. The first display
shows the results for the forecast information and then the forecasted
time series of the Sale variable in the Pricedata data set.
The Date column contains
the value of the time stamp. Observed values of the time series are
identified by a nonmissing value for the variable named Actual variable.
For example, the mean value of Sale at Date=13880 is 355.00. The
Predict column contains the predicted value under the chosen model
and the Residual column is the difference between the observed value
in the Actual column and the predicted value.
The StdErrPred column
contains the standard error of the predicted value. This is a measure
of the precision of predicting the value of Sale for the particular
time stamp under the model used. The Lower and Upper columns are the
confidence limits for the prediction.
The observations with
missing values for column Actual at the end of the table contain the
forecasted value in column Predict. Notice how the value of the prediction
standard error grows quickly as the forecast extends beyond the observed
time stamps. The width of the confidence interval grows accordingly.
The further that you predict into the future, the less precise the
prediction is. The result table contains several columns not shown
in the following display. These columns identify the table, the analysis
variable, and the aggregator. You can materialize those columns by
writing the table to a SAS data set.
The second FORECAST
statement specifies independent variables in the data. In this case,
the server performs time series model building and variable selection
and then returns the best-fitting time series model and values for
the selected independent variables.
The forecast information
table indicates that an ARIMA model with variable Price as the independent
variable was chosen as the best-fitting model. Note that in automatic
modeling mode it is possible that none of the independent variables
specified in the INDEP= option are used in the final model. The model
then falls back to an exponential smoothing model as in previous FORECAST
statement.
In addition, when one
or more independent variables are selected for the model, the output
includes a table with the values for the independent variables. Notice
that the independent variables are also forecast into the lead horizon.
The last time stamp in the input data set for the dependent and independent
variables is Date=15675 with Price having an observed value of 52.3.