Efficient data augmentation techniques for state space models

In the first part of the article, we propose a data augmentation scheme for improving the rate of convergence of the EM algorithm in estimating Gaussian state space models. The scheme considers a linear transformation of the latent states in which two working parameters are introduced for rescaling and recentering. We derive optimal values of the working parameters by minimizing the fraction of missing information, and study their large sample properties and dependence on the persistence and signal-to-noise ratio. An alternating expectation-conditional maximization (AECM) algorithm is designed to take advantage of the proposed scheme, and shown to be a more attractive alternative to the centered parametrization (CP) or noncentered parametrization (NCP). In the second part, we extend earlier results to Bayesian Markov chain Monte Carlo (MCMC) algorithms for non-Gaussian state space models, focusing on the stochastic volatility and stochastic conditional duration models. A block-specific reparametrization (BSR) strategy for multi-block MCMC samplers is proposed which enables the EM data augmentation scheme to be applied to non-Gaussian models via a mixture of normals approximation. Applications on simulated data and benchmark real data sets indicate that the BSR strategy is able to yield improvements in simulation efficiency compared with the CP or NCP, and sometimes even over ASIS (which interweaves the CP and NCP).