The FORECAST Procedure

Example 16.2 Forecasting Retail Sales

This example uses the stepwise autoregressive method to forecast the monthly U. S. sales of durable goods (DURABLES) and nondurable goods (NONDUR) from the SASHELP.USECON data set. The data are from Business Statistics, published by the U.S. Bureau of Economic Analysis. The following statements plot the series:

title1 'Sales of Durable and Nondurable Goods';
title2 'Plot of Forecast from WINTERS Method';
proc sgplot data=sashelp.usecon;
   series x=date y=durables / markers markerattrs=(symbol=circlefilled);
   xaxis values=('1jan80'd to '1jan92'd by year);
   yaxis values=(60000 to 150000 by 10000);
   format date year4.;
run;

title1 'Sales of Durable and Nondurable Goods';
title2 'Plot of Forecast from WINTERS Method';
proc sgplot data=sashelp.usecon;
   series x=date y=nondur / markers markerattrs=(symbol=circlefilled);
   xaxis values=('1jan80'd to '1jan92'd by year);
   yaxis values=(70000 to 130000 by 10000);
   format date year4.;
run;

The plots are shown in Output 16.2.1 and Output 16.2.2.

Output 16.2.1: Durable Goods Sales

Output 16.2.2: Nondurable Goods Sales

The following statements produce the forecast:

title1 "Forecasting Sales of Durable and Nondurable Goods";

proc forecast data=sashelp.usecon interval=month
              method=stepar trend=2 lead=12
              out=out outfull outest=est;
   id date;
   var durables nondur;
   where date >= '1jan80'd;
run;

The following statements print the OUTEST= data set.

title2 'OUTEST= Data Set: STEPAR Method';
proc print data=est;
run;

The PROC PRINT listing of the OUTEST= data set is shown in Output 16.2.3.

Output 16.2.3: The OUTEST= Data Set Produced by PROC FORECAST

Forecasting Sales of Durable and Nondurable Goods

OUTEST= Data Set: STEPAR Method

Obs	_TYPE_	DATE	DURABLES	NONDUR
1	N	DEC91	144	144
2	NRESID	DEC91	144	144
3	DF	DEC91	137	139
4	SIGMA	DEC91	4519.451	2452.2642
5	CONSTANT	DEC91	71884.597	73190.812
6	LINEAR	DEC91	400.90106	308.5115
7	AR01	DEC91	0.5844515	0.8243265
8	AR02	DEC91	.	.
9	AR03	DEC91	.	.
10	AR04	DEC91	.	.
11	AR05	DEC91	.	.
12	AR06	DEC91	0.2097977	.
13	AR07	DEC91	.	.
14	AR08	DEC91	.	.
15	AR09	DEC91	.	.
16	AR10	DEC91	-0.119425	.
17	AR11	DEC91	.	.
18	AR12	DEC91	0.6138699	0.8050854
19	AR13	DEC91	-0.556707	-0.741854
20	SST	DEC91	4.923E10	2.8331E10
21	SSE	DEC91	1.88157E9	544657337
22	MSE	DEC91	13734093	3918398.1
23	RMSE	DEC91	3705.9538	1979.4944
24	MAPE	DEC91	2.9252601	1.6555935
25	MPE	DEC91	-0.253607	-0.085357
26	MAE	DEC91	2866.675	1532.8453
27	ME	DEC91	-67.87407	-29.63026
28	RSQUARE	DEC91	0.9617803	0.9807752

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

title1 'Plot of Forecasts from STEPAR Method';
proc sgplot data=out;
   series x=date y=durables / group=_type_;
   xaxis values=('1jan90'd to '1jan93'd by qtr);
   yaxis values=(100000 to 150000 by 10000);
   refline '15dec91'd / axis=x;
run;

proc sgplot data=out;
   series x=date y=nondur / group=_type_;
   xaxis values=('1jan90'd to '1jan93'd by qtr);
   yaxis values=(100000 to 140000 by 10000);
   refline '15dec91'd / axis=x;
run;

The plots are shown in Output 16.2.4 and Output 16.2.5.

Output 16.2.4: Forecast of Durable Goods Sales

Output 16.2.5: Forecast of Nondurable Goods Sales