A0321
Title: Unobserved component models, approximate filters and dynamic adaptive mixture models
Authors: Alessandra Luati - Imperial College London (United Kingdom) [presenting]
Leopoldo Catania - Aarhus BBS (Denmark)
Enzo DInnocenzo - VU University Amsterdam (Netherlands)
Abstract: State estimation in unobserved component models with parameter uncertainty is traditionally performed through approximate filters, where Gaussian distributions with given moments are employed to replace otherwise intractable conditional densities. The purpose is to re-examine signal-plus-noise models where parameter uncertainty is induced by a latent variable that may assume a fixed number of states. First, it is shown that, for these models, the approximate filters commonly adopted in the literature can be obtained as linear combinations of minimum variance linear unbiased estimators. Second, it is observed that they coincide with filters implied by a novel class of dynamic adaptive mixture models, where the parameters of a mixture of distributions evolve over time following a recursion that is based on the score of the one-step-ahead predictive distribution. Focusing on a robust specification, where the mixture components are Student's t distributions, it proves the existence, stationarity and ergodicity of the data-generating process as well as the invertibility of the filter and consistency and asymptotic normality of the maximum likelihood estimator of the static parameters. An application to a climate time series dataset is discussed, where the novel specification is compared with and shown to outperform robust score-driven filters and the related class of mixture autoregressive models.
