Leopoldo Catania, Aarhus BSS and CREATES
Project Description/Abstract
State estimation in unobserved component models with parameter uncertainty is traditionally performed through approximate filters based on collapsing schemes, where Gaussian distributions with given moments are employed to replace otherwise intractable conditional densities. This paper considers a signal plus noise model where parameter uncertainty is induced by a latent variable that may assume a fixed number of states. We show that for these models, the approximated filter commonly adopted coincides with the one implied by the dynamic adaptive mixture model (DAMM) specification. In dynamic adaptive mixture models, 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. When the components of the mixture are Gaussian, the score update coincides with a conditionally linear estimator that is unbiased and minimizes the conditional prediction error variances of the state variable, leading to improved efficiency when compared with a standard minimum variance unbiased linear estimate.
The paper then focuses on a robust DAMM specification, where the mixture components are Student’s t distributions. The stochastic properties of the filter and asymptotic properties of the maximum likelihood estimator of the static parameters are derived. The finite sample properties are investigated through a simulation study and an application to the US industrial production index, where the novel specification is compared with the alternative class of mixture autoregressive models is provided.
Co-authors
Enzo D’Innocenzo, Vrije Universiteit Amsterdam
Alessandra Luati, University of Bologna