The response variables in time series analysis are often classified as either stock variables or flow variables. Stock variables, such as interest rates or temperatures, are measured at a particular point in time. Flow variables, such as monthly income or weekly sales, are defined with respect to an interval of time. Flow variables have the property that they remain meaningful under the operations of temporal aggregation and temporal distribution—for example, aggregation of daily sales to weekly sales and distribution (or dis-aggregation) of weekly sales to daily sales are quite natural, whereas the same cannot be said of temperature readings. This section explains how you can use the SSM procedure to do model-based temporal aggregation and distribution of flow variables. State space models are often used to carry out model-based temporal aggregation and distribution. Two properties of state space models make them particularly suitable for this purpose:
If a variable is modeled by a state space model at a particular time interval, its aggregated form—for example, daily to monthly—also follows a state space model. Moreover, the state space forms of these two models have a simple relationship.
State space models can easily handle missing response values.
The discussion in this section, which is based on Harvey (1989, chap. 6, sec. 3), is limited to regular data types—that is, the data must be either univariate or multivariate time series.