Overview: SSM Procedure

(Linear) state space models (SSMs) are often used for analyzing continuous response variables that are recorded sequentially according to a numeric indexing variable. In many cases the indexing variable is time, and the observations are collected at regular time intervals—for example, hourly, weekly, or monthly. In such cases the resulting data are called time series data. In other cases the indexing variable might not be time, or the observations might not be equally spaced according to the indexing variable. These more general types of sequential data are called longitudinal data. Because of their sequential nature, these types of data exhibit some characteristic features. For example, chronologically closer measurements tend to be highly correlated while measurements farther apart are essentially uncorrelated, and data can be trending in a particular direction and can have seasonal or other periodic patterns. SSMs are specially designed to model such sequential data. They are applicable in both univariate and multivariate response situations and can easily incorporate predictor (independent variable) information when it is available.

The SSM procedure performs state space modeling of univariate and multivariate time series and longitudinal data. You can do the following with the SSM procedure:

• analyze a very general linear state space model

• use an expressive language to specify an SSM. An SSM specification consists of specifying a variety of matrices—for example, the state transition matrix and the covariance matrices of the state and observation disturbances. The SSM procedure provides language similar to a DATA step for specifying the elements of these matrices. The matrix elements can be user-defined functions of data variables and unknown parameters.

• easily specify several commonly needed univariate and multivariate SSMs by using only a few keywords. These include the principal univariate and multivariate structural models for regularly spaced data, and a variety of trend and cycle models for the longitudinal data.

• estimate unknown model parameters by (restricted) maximum likelihood. The likelihood function is computed by using the (diffuse) Kalman filter algorithm.

• output to a data set the series forecasts, residuals, and the full sample estimates of any linear combination of the underlying state variables. These estimates are obtained by using the (diffuse) Kalman filter and smoother algorithm.