Joint Independent Metropolis-Hastings Methods for Nonlinear Non-Gaussian State Space Models

Arbeitspapier

We propose a new methodology for the Bayesian analysis of nonlinear non-Gaussian state space models with a Gaussian time-varying signal, where the signal is a function of a possibly high-dimensional state vector. The novelty of our approach is the development of proposal densities for the joint posterior density of parameter and state vectors: a mixture of Student's t-densities as the marginal proposal density for the parameter vector, and a Gaussian density as the conditional proposal density for the signal given the parameter vector. We argue that a highly efficient 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 an estimate of the marginal likelihood are obtained directly as an output of the algorithm. Our methods are computationally efficient and produce more accurate estimates when compared to recently proposed alternativ es. 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 return data and corporate default panel data.

Object Details

• Language: Englisch

References and Relationships

• Bibliographic citation: Series: Tinbergen Institute Discussion Paper ; No. 13-050/III

Classification and Topics

• Classification: Wirtschaft ; Bayesian Analysis: General ; Statistical Simulation Methods: General ; Single Equation Models; Single Variables: Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes ; Multiple or Simultaneous Equation Models: Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models ; Financial Econometrics
• Subject: nonlinear non-Gaussian state space model ; Bayesian inference ; Monte Carlo estimation ; Metropolis-Hastings algorithm ; mixture of Student's t-distributions

Contributors, Places and Time

• Event: Geistige Schöpfung
• (who): Barra, Istvan ; Hoogerheide, Lennart ; Koopman, Siem Jan ; Lucas, Andre
• Event: Veröffentlichung
• (who): Tinbergen Institute
• (where): Amsterdam and Rotterdam
• (when): 2012

Further information

• Handle: http://hdl.handle.net/10419/87411
• Last update: 10.03.2025, 11:45 AM CET