Joint Bayesian Analysis of Parameters and States in Nonlinear, Non-Gaussian State Space Models - István Barra; Lennart Hoogerheide; Siem Jan Koopman; André Lucas (Tinbergen Institute, 2014)
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. A particular feature of our approach is that smoothed estimates of the states and the marginal likelihood are obtained directly as an output of the algorithm. Our method provides a computationally efficient alternative to several recently proposed algorithms. We present extensive simulation evidence for stochastic volatility and stochastic intensity models. For our empirical study, we analyse the performance of our method for stock returns and corporate default panel data. (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.)
Keywords: C11; C15; C22; C32; C58; 330; Bayesian inference; importance sampling; Monte Carlo estimation; Metropolis-Hastings algorithm; mixture of Student's t-distributions