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This paper demonstrates the practical application of recently developed techniques of efficient numerical analysis for dynamic models. The models presented share a common basic structural foundation but nevertheless cover a very large arena of possible applications, as will be shown.

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Ahstract. We consider the analysis of normal dynamic linear models subject to reference (vague or Uninformative) initial priors on the state parameters and observational variance. New sequential updating equations and the related smoothing or filtering recurrences are derived for such reference analyses. The case of no evolution noise is highlighted, as this is of key practical importance and interest. Practical questions concerning prediction and collinearity are discussed, as are particular features of special models.