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Exponential family state space models based on a conjugate latent process

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  • P. Vidoni

Abstract

This paper introduces non‐linear and non‐Gaussian state space models with analytic updating recursions for filtering and prediction. This new class of models involves some well‐known results in the theory of exponential models and of exponential dispersion models and the latent process is defined in such a way that both the filtering and the prediction distributions turn out to be conjugate to the observation distribution at each step. The corresponding analytic and inferential properties are investigated and some simple examples are presented.

Suggested Citation

  • P. Vidoni, 1999. "Exponential family state space models based on a conjugate latent process," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(1), pages 213-221.
    • Handle: RePEc:bla:jorssb:v:61:y:1999:i:1:p:213-221
    DOI: 10.1111/1467-9868.00172
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    Cited by:

    1. Kostas Triantafyllopoulos, 2009. "Inference of Dynamic Generalized Linear Models: On‐Line Computation and Appraisal," International Statistical Review, International Statistical Institute, vol. 77(3), pages 430-450, December.
    2. de Pinho, Frank M. & Franco, Glaura C. & Silva, Ralph S., 2016. "Modeling volatility using state space models with heavy tailed distributions," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 119(C), pages 108-127.
    3. Ferrante, Marco & Vidoni, Paolo, 1999. "A Gaussian-generalized inverse Gaussian finite-dimensional filter," Stochastic Processes and their Applications, Elsevier, vol. 84(1), pages 165-176, November.
    4. Yang Lu, 2020. "A simple parameter‐driven binary time series model," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 39(2), pages 187-199, March.
    5. Vidoni Paolo, 2004. "Constructing Non-linear Gaussian Time Series by Means of a Simplified State Space Representation," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 8(2), pages 1-20, May.
    6. T. R. Santos, 2018. "A Bayesian GED-Gamma stochastic volatility model for return data: a marginal likelihood approach," Papers 1809.01489, arXiv.org.
    7. Ferrante, Marco & Frigo, Nadia, 2009. "Particle filtering approximations for a Gaussian-generalized inverse Gaussian model," Statistics & Probability Letters, Elsevier, vol. 79(4), pages 442-449, February.
    8. Kuk, Anthony Y. C., 1999. "The use of approximating models in Monte Carlo maximum likelihood estimation," Statistics & Probability Letters, Elsevier, vol. 45(4), pages 325-333, December.

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