Example 3.3 A Generic Seasonal Model Specification Suitable for Different Season Lengths

In the case of many seasonal model specifications, it is possible to describe a generic specification that is applicable in a variety of situations just by changing the season length specifications at appropriate places. As an example, consider the Airline model, which is very useful for modeling seasonal data. The Airline model for a monthly series can be specified using the following syntax:

   proc hpfarimaspec repository=work.specs
                     name=MonthlyAirline
        label="Airline Model For A Series With Season Length 12";
      forecast symbol=Y q=(1)(1)12 dif=(1, 12) noint
               transform= log;
   run;

It is easy to see that the same syntax is applicable to a quarterly series if the multiplier in the MA specification is changed from 12 to 4 and the seasonal differencing order is similarly changed from 12 to 4. A generic specification that allows for late binding of season lengths can be generated by the following syntax:

   proc hpfarimaspec repository=work.specs
                     name=GenericAirline
                     label="Generic Airline Model";
       forecast symbol=Y q=(1)(1)s dif=(1, s) noint
                transform= log;
   run;

In this syntax the multiplier in the MA specification is changed from 12 to "s", and similarly the seasonal differencing order 12 is changed to "s". This syntax creates a template for the Airline model that is applicable to different season lengths. When the HPFENGINE procedure, which actually uses such model specifications to estimate the model and produce the forecasts, encounters such "generic" specification it automatically creates a proper specification by replacing the placeholders for the seasonal multiplier and the seasonal differencing order with the value implied by the ID variable or its SEASONALITY= option. The following example illustrates the use of this generic spec. It shows how the same spec can be used for monthly and quarterly series. The parameter estimates for monthly and quarterly series are given in Output 3.3.1 and Output 3.3.2, respectively.

   /* Create a selection list that contains
      the Generic Airline Model */
   
   proc hpfselect repository=work.specs
                  name=genselect;
      spec GenericAirline;
   run;

   /* Monthly interval */
   
   proc hpfengine data=sashelp.air
                  repository=work.specs
                  globalselection=genselect
                  print=(estimates);
      id date interval=month;
      forecast air;
   run;