On markov chain monte carlo methods for nonlinear and non-gaussian state-space models

Abstract

In this paper, a nonlinear and/or non‐Gaussian smoother utilizing Markov chain Monte Carlo Methods is proposed, where the measurement and transition equations are specified in any general formulation and the error terms in the state‐space model are not necessarily normal. The random draws are directly generated from the smoothing densities. For random number generation, the Metropolis‐Hastings algorithm and the Gibbs sampling technique are utilized. The proposed procedure is very simple and easy for programming, compared with the existing nonlinear and non‐Gaussian smoothing techniques. Moreover, taking several candidates of the proposal density function, we examine precision of the proposed estimator.

Keywords:

• Nonlinear and Non‐Gaussian State‐Space Models
• Filtering
• Smoothing
• Markov Chain Monte Carlo
• Gibbs Sampling
• Metropolis‐Hastings Algorithm