SEM modeling with singular moment matrices, Part I: ML-Estimation of time series

A structural equation model (SEM) with deterministic intercepts isintroduced. The gaussian likelihood function does not contain determinantsof sample moment matrices and is thus well dened for only onestatistical unit. The SEM is applied to the dynamic state space model andcompared with the Kalman lter (KF) approach. The likelihoods of bothmethods are shown to be equivalent, but for long time series numericalproblems occur in the SEM approach, which are traced to the inversionof the latent state covariance matrix.[...]