## 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)

### Citations:

Zbl 0519.62029; Zbl 0619.62029
Full Text:

### References:

 [1] Anderson B. O. D., Optimal Filtering. (1979) · Zbl 0688.93058 [2] Broemeling L., Bayesian Analysis of Linear Models. (1985) · Zbl 0564.62020 [3] DOI: 10.2307/2290282 [4] Dempster A. P., J. R. Statist. Soc. Ser. B 39 pp 1– (1977) [5] Fruhwirth-Schnatter S., J. R. Statist. Soc. Ser. B. (1994) [6] Harrison P. J., J. R. Statist. Soc. Ser. B 38 pp 205– (1976) [7] Harvey A., Forecasting, Structural Time Series Models, and the Kalman Filter. (1989) [8] Liptser R. S., Statistics of Random Processes. (1977) · Zbl 0364.60004 [9] DOI: 10.1109/TAC.1965.1098191 [10] Pole A., Bayesian Statistics 3 pp 733– (1988) [11] Tanner M., Tools for Statistical Inference. Observed Data and Data Augmentation Methods. Lecture Notes in Statistics 67. (1991) · Zbl 0724.62003 [12] DOI: 10.2307/2289457 · Zbl 0619.62029 [13] West M., Bayesian Forecasting and Dynamic Models. (1989) · Zbl 0697.62029
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