Exponential family state space models based on a conjugate latent process

Journal of the Royal Statistical Society: Series B (Statistical Methodology) · 1999 · Volume 61 · Issue 1

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.

Keywords

Conjugate exponential distribution, Exponential dispersion model, Finite dimensional filter, Gaussian local scale model, Recursive updating

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