SSM Procedure

(View the complete code for this example.)

This example illustrates how you can do model-based temporal aggregation of a response variable. The following DATA step creates a data set, Nile, by using a well-known data set that contains annual recordings of the Nile water level measured between the years 1871 and 1970. The Nile water level is clearly a stock variable, and temporal aggregation of such variables is usually meaningless. However, for illustration purposes, assume that you are interested in forecasting triannual totals of the water level.

data Nile;
   input level @@;
   year = intnx( 'year', '1jan1871'd, _n_-1 );
   format year year4.;
   startAggr = (mod(_n_, 3) = 1);
datalines;
1120  1160  963  1210  1160  1160  813  1230   1370  1140
995   935   1110 994   1020  960   1180 799    958   1140
1100  1210  1150 1250  1260  1220  1030 1100   774   840
874   694   940  833   701   916   692  1020   1050  969
831   726   456  824   702   1120  1100 832    764   821
768   845   864  862   698   845   744  796    1040  759
781   865   845  944   984   897   822  1010   771   676
649   846   812  742   801   1040  860  874    848   890
744   749   838  1050  918   986   797  923    975   815
1020  906   901  1170  912   746   919  718    714   740
. . . . . . .
;

The Nile date set contains three variables: year indicates the observation year, level contains the yearly water level, and startAggr is a dummy variable that indicates the start of the triannual aggregation intervals. It is known that for the time span of the observations, the yearly water levels can be reasonably modeled as a sum of a random walk trend, a level shift in the year 1899, and the observation error. The following statements show you how to obtain forecasts of the triannual water level that are consistent with the model postulated for the yearly water levels:

proc ssm data=Nile;
  id year interval=year;
  shift1899 = ( year >= '1jan1899'd );
  trend rw(rw);
  irregular wn;
  model level = shift1899 RW wn  / aggregate(start=startAggr);
  output out=nileOut;
quit;

As a result of running this program, you get the usual output that is associated with fitting the specified model to the yearly water level. In addition (as explained in the section Temporal Aggregation), the AGGREGATE option in the MODEL statement causes the estimation and printing of triannual aggregates of the water level. Output 33.17.1 shows the last few rows of this output. When the summands—the response values—in the aggregation are known, the aggregation can be done without error; that is, the standard error of the estimation is zero. However, when at least one summand in the aggregate is missing, the standard error of estimation is nonzero.