The SSM Procedure

Multivariate White Noise

The STATE statement option TYPE=WN specifies white noise of dimension dim—that is, a sequence of zero mean, independent, Gaussian vectors with covariance $\pmb {\Sigma }$ . The specification of the associated system matrices is trivial: $\mb{T}$ is zero, $\mb{Q} = \pmb {\Sigma }$ , and the initial condition is nondiffuse ( $\mb{Q}_{1} = \pmb {\Sigma }$ and $\mb{A}_{1} = 0$ ).

Multivariate white noise is needed to specify the observation equation noise term for the multivariate models for the time series data. Since the state space formulation for the SSM procedure requires the observation equation noise vector to have the diagonal form, you need to include the noise vector in the state. The noise term for the ith response variable is defined by a component that simply picks the ith element of this multivariate white noise. For example, the component wn_i defined as follows can be used as a noise term in the MODEL statement of the ith response variable:

     state white(dim) type=wn ...;
     component wn_3 = white[3];