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Data augmentation and dynamic linear models. (English) Zbl 0815.62065

Summary: We define a subclass of dynamic linear models with unknown hyperparameter called \(d\)-inverse-gamma models. We then approximate the marginal probability density functions of the hyperparameter and the state vector by the data augmentation algorithm of M. Tanner and W. H. Wong [J. Am. Stat. Assoc. 82, 528-541 (1987; Zbl 0619.62029)]. We prove that the regularity conditions for convergence hold. For practical implementation a forward-filtering-backward-sampling algorithm is suggested, and the relation to Gibbs sampling is discussed in detail.

MSC:

62M20 Inference from stochastic processes and prediction
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
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