# The FORECAST Procedure

### Example 16.1 Forecasting Auto Sales

This example uses the Winters method to forecast the monthly U. S. sales of passenger cars series (VEHICLES) from the data set SASHELP.USECON. These data are taken from Business Statistics, published by the U. S. Bureau of Economic Analysis.

The following statements plot the series. The plot is shown in Output 16.1.1.

```title1 "Sales of Passenger Cars";

symbol1 i=spline v=dot;
axis2 label=(a=-90 r=90 "Vehicles and Parts" )
order=(6000 to 24000 by 3000);

title1 "Sales of Passenger Cars";
proc sgplot data=sashelp.usecon;
series x=date y=vehicles / markers;
xaxis values=('1jan80'd to '1jan92'd by year);
yaxis values=(6000 to 24000 by 3000);
format date year4.;
run;
```

Output 16.1.1: Monthly Passenger Car Sales

The following statements produce the forecast:

```proc forecast data=sashelp.usecon interval=month
out=out outfull outresid outest=est;
id date;
var vehicles;
where date >= '1jan80'd;
run;
```

The INTERVAL=MONTH option indicates that the data are monthly, and the ID DATE statement gives the dating variable. The METHOD=WINTERS specifies the Winters smoothing method. The LEAD=12 option forecasts 12 months ahead. The OUT=OUT option specifies the output data set, while the OUTFULL and OUTRESID options include in the OUT= data set the predicted and residual values for the historical period and the confidence limits for the forecast period. The OUTEST= option stores various statistics in an output data set. The WHERE statement is used to include only data from 1980 on.

The following statements print the OUT= data set (first 20 observations):

```title2 'The OUT= Data Set';
proc print data=out (obs=20) noobs;
run;
```

The listing of the output data set produced by PROC PRINT is shown in part in Output 16.1.2.

Output 16.1.2: The OUT= Data Set Produced by PROC FORECAST (First 20 Observations)

 Sales of Passenger Cars The OUT= Data Set

JAN80 ACTUAL 0 8808.00
JAN80 FORECAST 0 8046.52
JAN80 RESIDUAL 0 761.48
FEB80 ACTUAL 0 10054.00
FEB80 FORECAST 0 9284.31
FEB80 RESIDUAL 0 769.69
MAR80 ACTUAL 0 9921.00
MAR80 FORECAST 0 10077.33
MAR80 RESIDUAL 0 -156.33
APR80 ACTUAL 0 8850.00
APR80 FORECAST 0 9737.21
APR80 RESIDUAL 0 -887.21
MAY80 ACTUAL 0 7780.00
MAY80 FORECAST 0 9335.24
MAY80 RESIDUAL 0 -1555.24
JUN80 ACTUAL 0 7856.00
JUN80 FORECAST 0 9597.50
JUN80 RESIDUAL 0 -1741.50
JUL80 ACTUAL 0 6102.00
JUL80 FORECAST 0 6833.16

The following statements print the OUTEST= data set:

```title2 'The OUTEST= Data Set: WINTERS Method';
proc print data=est;
run;
```

The PROC PRINT listing of the OUTEST= data set is shown in Output 16.1.3.

Output 16.1.3: The OUTEST= Data Set Produced by PROC FORECAST

 Sales of Passenger Cars The OUTEST= Data Set: WINTERS Method

Obs _TYPE_ DATE VEHICLES
1 N DEC91 144
2 NRESID DEC91 144
3 DF DEC91 130
4 WEIGHT1 DEC91 0.1055728
5 WEIGHT2 DEC91 0.1055728
6 WEIGHT3 DEC91 0.25
7 SIGMA DEC91 1741.481
8 CONSTANT DEC91 18577.368
9 LINEAR DEC91 4.804732
10 S_JAN DEC91 0.8909173
11 S_FEB DEC91 1.0500278
12 S_MAR DEC91 1.0546539
13 S_APR DEC91 1.074955
14 S_MAY DEC91 1.1166121
15 S_JUN DEC91 1.1012972
16 S_JUL DEC91 0.7418297
17 S_AUG DEC91 0.9633888
18 S_SEP DEC91 1.051159
19 S_OCT DEC91 1.1399126
20 S_NOV DEC91 1.0132126
21 S_DEC DEC91 0.802034
22 SST DEC91 2.63312E9
23 SSE DEC91 394258270
24 MSE DEC91 3032755.9
25 RMSE DEC91 1741.481
26 MAPE DEC91 9.4800217
27 MPE DEC91 -1.049956
28 MAE DEC91 1306.8534
29 ME DEC91 -42.95376
30 RSQUARE DEC91 0.8502696

The following statements plot the residuals. The plot is shown in Output 16.1.4.

```title1 "Sales of Passenger Cars";
title2 'Plot of Residuals';
proc sgplot data=out;
where _type_ = 'RESIDUAL';
needle x=date y=vehicles / markers markerattrs=(symbol=circlefilled);
xaxis values=('1jan80'd to '1jan92'd by year);
format date year4.;
run;
```

Output 16.1.4: Residuals from Winters Method

The following statements plot the forecast and confidence limits. The last two years of historical data are included in the plot to provide context for the forecast plot. A reference line is drawn at the start of the forecast period.

```title1 "Sales of Passenger Cars";
title2 'Plot of Forecast from WINTERS Method';
proc sgplot data=out;
series x=date y=vehicles / group=_type_ lineattrs=(pattern=1);
where _type_ ^= 'RESIDUAL';
refline '15dec91'd / axis=x;
yaxis values=(9000 to 25000 by 1000);
xaxis values=('1jan90'd to '1jan93'd by qtr);
run;
```

The plot is shown in Output 16.1.5.

Output 16.1.5: Forecast of Passenger Car Sales