The new experimental SSM procedure enables linear state space modeling of time series and longitudinal data. An important feature of the SSM procedure is a modeling language that permits easy specification of possibly complex state space models. In particular, the system matrices—such as the state transition matrix and the covariance of the state disturbance—can be time-varying and their elements can depend on user-specified parameters in a complex way. Often a state space model can be specified by combining simpler submodels. This modeling language is especially suited for specification of such models. The following list identifies the key features of the SSM procedure:
Many commonly needed state space models, such as the basic univariate and multivariate structural time series models, can be easily specified using a few keywords. Similarly, models for panel data can also be easily specified.
The unknown model parameters are estimated by (restricted) maximum likelihood and a variety of likelihood-based information criteria are reported for model diagnostics.
One-step-ahead and full-sample estimates of various state effects (linear combinations of the underlying state vector) and one-step-ahead residuals can be output to a data set. In particular, model-based forecasts, backcasts, interpolated missing values of the response variables, and the estimates of the latent effects such as trend, cycles, and seasonals, can be output to a data set. These estimates are generated by using the Kalman filtering and smoothing algorithm.
State space modeling is commonly used for the analysis of regularly spaced univariate and multivariate time series data. In fact, state space modeling is quite useful for irregularly spaced—possibly with replicate measurements—longitudinal data also. An important feature of the SSM procedure is that it enables analysis of such longitudinal data, in addition to the regularly spaced univariate and multivariate time series data. Several trend models suitable for longitudinal data analysis can be easily specified using a few keywords.