Convergence and the Constant Dynamic Linear Model

It is well known that, as calculated using the Kalman filter recurrence relationships, the posterior parameter variance and the adaptive vector of observable constant dynamic linear models converge to limiting values. However, most proofs are tortuous, some have subtle errors and some relate only to specific cases. An elegant probabilistic convergence proof demonstrates that the limit is independent of the initial parametric prior. The result is extended to a class of multivariate dynamic linear models. Finally the proof is shown to apply to many non-observable constant DLMs. © 1997 John Wiley & Sons, Ltd.