The ESM Procedure

## Example 13.1 Forecasting of Time Series Data

This example uses retail sales data to illustrate how the ESM procedure can be used to forecast time series data.

The following DATA step creates a data set from data recorded monthly at numerous points of sales. The data set, SALES, contains a variable DATE that represents time and a variable for each sales item. Each value of the DATE variable is recorded in ascending order, and the values of each of the other variables represent a single time series:

```   data sales;
format date date9.;
input date : date9. shoes socks laces dresses
coats shirts ties belts hats blouses;
datalines;

... more lines ...

```

The following ESM procedure statements forecast each of the monthly time series:

```   proc esm data=sales out=nextyear;
id date interval=month;
forecast _numeric_;
run;
```

The preceding statements generate forecasts for every numeric variable in the input data set SALES for the next twelve months and store these forecasts in the output data set NEXTYEAR.

The following statements plot the forecasts:

```   title1 "Shoe Department Sales";
proc sgplot data=nextyear;
series x=date y=shoes / markers
markerattrs=(symbol=circlefilled color=red)
lineattrs=(color=red);
series x=date y=socks / markers
markerattrs=(symbol=asterisk color=blue)
lineattrs=(color=blue);
series x=date y=laces / markers
markerattrs=(symbol=circle color=styg)
lineattrs=(color=styg);
refline '01JAN1999'd / axis=x;
xaxis values=('01JAN1994'd to '01DEC2000'd by year);
yaxis values=(2000 to 10000 by 1000) minor label='Websites';
run;
```

The plots are shown in Output 13.1.1. The historical data is shown to the left of the reference line and the forecasts for the next twelve monthly periods is shown to the right.

Output 13.1.1 Retail Sales Forecast Plots

The default simple exponential smoothing model is used because the MODEL= option is omitted on the FORECAST statement. Note that for simple exponential smoothing the forecasts are constant.

The following ESM procedure statements are identical to the preceding statements except that the PRINT=FORECASTS option is specified:

```   proc esm data=sales out=nextyear print=forecasts;
id date interval=month;
forecast _numeric_;
run;
```

In addition to forecasting each of the monthly time series, the preceding statements print the forecasts by using the Output Delivery System (ODS); the forecasts are partially shown in Output 13.1.2. This output shows the predictions, prediction standard errors, and the upper and lower confidence limits for the next twelve monthly periods.

Output 13.1.2 Forecast Tables
 Shoe Department Sales

The ESM Procedure

Forecasts for Variable shoes
Obs Time Forecasts Standard Error 95% Confidence Limits
62 FEB1999 6009.1986 1069.4059 3913.2016 8105.1956
63 MAR1999 6009.1986 1075.7846 3900.6996 8117.6976
64 APR1999 6009.1986 1082.1257 3888.2713 8130.1259
65 MAY1999 6009.1986 1088.4298 3875.9154 8142.4818
66 JUN1999 6009.1986 1094.6976 3863.6306 8154.7666
67 JUL1999 6009.1986 1100.9298 3851.4158 8166.9814
68 AUG1999 6009.1986 1107.1269 3839.2698 8179.1274
69 SEP1999 6009.1986 1113.2895 3827.1914 8191.2058
70 OCT1999 6009.1986 1119.4181 3815.1794 8203.2178
71 NOV1999 6009.1986 1125.5134 3803.2329 8215.1643
72 DEC1999 6009.1986 1131.5758 3791.3507 8227.0465
73 JAN2000 6009.1986 1137.6060 3779.5318 8238.8654

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