Joint Bayesian Analysis of Parameters and States in Nonlinear, Non-Gaussian State Space Models

Abstract

We propose a new methodology for designing flexible proposal densities for the joint posterior density of parameters and states in a nonlinear, non-Gaussian state space model. We show that a highly efficient Bayesian procedure emerges when these proposal densities are used in an independent Metropolis-Hastings algorithm or in importance sampling. Our method provides a computationally more efficient alternative to several recently proposed algorithms. We present extensive simulation evidence for stochastic intensity and stochastic volatility models based on Ornstein-Uhlenbeck processes. For our empirical study, we analyse the performance of our methods for corporate default panel data and stock index returns.(This paper is an updated version of the paper that appeared earlier as Barra, I., Hoogerheide, L.F., Koopman, S.J., and Lucas, A. (2013) Joint Independent Metropolis-Hastings Methods for Nonlinear Non-Gaussian State Space Models. TI Discussion Paper 13-050/III. Amsterdam: Tinbergen Institute.)