The SSM Procedure (Experimental)
-
Overview
- Getting Started
-
Syntax
-
DetailsState Space Model and NotationTypes of Data OrganizationOverview of Model Specification SyntaxLikelihood, Filtering, and SmoothingContrasting 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 Two-Way Random-Effects and Autoregressive Model for Panel DataBackcasting, Forecasting, and InterpolationSmoothing of Repeated Measures DataA User-Defined Trend ModelModel with Multiple ARIMA ComponentsDynamic Factor ModelingDiagnostic PlotsVariable Bandwidth Smoothing
- References
Covariance Parameterization
The covariance matrices specified by the COV and COV1 options in the STATE statement must be positive semidefinite. When these matrices are of general form and are not user-specified,
they are internally parameterized by their Cholesky root. Suppose that 
, an 
positive semidefinite matrix of rank 
, is such a covariance matrix. Then, can always be written as
![\[ \Sigma = R R^{} \]](images/etsug_ssm0446.png){kind=small} |
where the (generalized) Cholesky root, 
, is an 
lower triangular matrix with nonnegative diagonal elements (that is, ![$R[i,j] = 0 \; \mr {if} j > i$](images/etsug_ssm0449.png){kind=small}
and ![$R[i,i] \geq 0,\; 1 \leq i \leq r$](images/etsug_ssm0450.png){kind=small}
). The SSM procedure parameterizes by the elements of its Cholesky root, which adds 
elements to the parameter vector 
.