A Non-Gaussian Family of State-Space Models with Exact Marginal Likelihood

• Activity Number: 604
• Type: Contributed
• Date/Time: Wednesday, August 7, 2013 : 2:00 PM to 3:50 PM
• Sponsor: International Society for Bayesian Analysis (ISBA)
• Author(s): Dani Gamerman*+ and Glaura da Conceição Franco and Thiago Rezende dos Santos
• Companies: Instituto De Matematica-UFRJ and Universidade Federal de Minas Gerais and Universidade Federal de Minas Gerais
• Keywords: Bayesian ; forecasting ; smoothing ; sampling methods ; non-linear models ; evolution disturbances

Abstract

The Gaussian assumption generally employed in many state space models is usually not satisfied for real time series. Thus, in this work a broad family of non-Gaussian models is defined by expanding previous work in the literature. The expansion is obtained at two levels: at the observational level it allows for many distributions not previously considered and at the latent state level it involves an expanded specification for the system evolution. The class retains analytical availability of the marginal likelihood function, uncommon outside Gaussianity. This expansion solves many previously existing problems such as long-term prediction, missing values and irregular temporal spacing. Inference about the state components can be performed due to the introduction of a new and exact smoothing procedure, in addition to filtered distributions. Inference for the hyperparameters is presented from the classical and Bayesian perspectives. The results seem to indicate competitive results of the models when compared to other non-Gaussian models available. The methodology is applied to Gaussian and non-Gaussian dynamic linear models with time-varying means and variances.