SSM Procedure

Temporal aggregation is the reverse of temporal distribution. In this case, the observations are available on a finer time scale, and you are interested in estimating the aggregated values on some coarser time scale—for example, estimating weekly totals from daily data. Of course, the aggregation is trivial in the historical region where the observations on the finer scale are known—in fact, in this case the estimation of the aggregate values is done with no estimation error. However, when the aggregate values are to be estimated in the region where the observations on the finer scale are missing—for example, in the forecast region—the problem becomes nontrivial. It is easier to explain the situation by using a simple example. Suppose denote the daily observations of a response variable, y. Let denote the within-week daily running totals—that is, represents the total of y values up to the day t in the week that contains the day t. Clearly, given the daily values the aggregate values are fully known. The question is, assuming that y follows a state space model, how do you estimate and obtain appropriate confidence intervals for in the forecast region ()? In this section you have already seen that when a variable is modeled by a state space model at a particular time interval, its aggregated form also follows a state space model. The AGGREGATE(START=) option in the MODEL statement of the SSM procedure enables you to perform temporal aggregation for a response variable. An illustration of such aggregation is shown in Example 33.17.