The SSM Procedure
-
Overview
- Getting Started
-
Syntax
-
DetailsState Space Model and NotationTypes of Sequence DataOverview of Model Specification SyntaxFiltering, Smoothing, Likelihood, and Structural Break DetectionEstimation of User-Specified Linear Combination of State ElementsContrasting PROC SSM with Other SAS Procedures Predefined Trend ModelsPredefined Structural ModelsCovariance ParameterizationMissing ValuesComputational IssuesDisplayed OutputODS Table NamesODS Graph NamesOUT= Data Set
-
ExamplesBivariate Basic Structural Model Panel Data: Random-Effects and Autoregressive ModelsBackcasting, Forecasting, and InterpolationLongitudinal Data: Smoothing of Repeated MeasuresA User-Defined Trend ModelModel with Multiple ARIMA ComponentsDynamic Factor ModelingDiagnostic Plots and Structural Break AnalysisLongitudinal Data: Variable Bandwidth SmoothingA Transfer Function Model for the Gas Furnace DataPanel Data: Dynamic Panel Model for the Cigar DataMultivariate Modeling: Long-Term Temperature TrendsBivariate Model: Sales of Mink and Muskrat FursFactor Model: Now-Casting the US EconomyLongitudinal Data: Lung Function Analysis
- References
The STATE statement option TYPE=RW specifies a dim-dimensional random walk
![\[ \pmb {\alpha }_{t+1} = \pmb {\alpha }_{t} + \pmb {\eta }_{t+1} \]](images/etsug_ssm0392.png){kind=small}
where 
is a sequence of zero mean, independent, Gaussian vectors with covariance 
. The specification of the associated system matrices is trivial: 
is a dim-dimensional identity matrix, 
, 
, and the initial condition is fully diffuse (
and 
).
The multivariate random walk is a useful trend model for multivariate time series data. The trend term for the ith response variable is defined by a component that simply picks the ith (
) element of 
. For example, the component rw_i defined as follows can be used as a trend term in the MODEL statement of the ith response variable:
state randomWalk(3) type=rw ...;
component rw_2 = randomWalk[2];