# The SSM Procedure

#### Multivariate Random Walk Trend

The STATE statement option TYPE=RW specifies a dim-dimensional random walk

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];