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

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Author Info

  • Istvan Barra

    (VU University Amsterdam)

  • Lennart Hoogerheide

    (VU University Amsterdam)

  • Siem Jan Koopman

    (VU University Amsterdam)

  • Andre Lucas

    (VU University Amsterdam)

Abstract

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.

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Bibliographic Info

Paper provided by Tinbergen Institute in its series Tinbergen Institute Discussion Papers with number 13-050/III.

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Date of creation: 26 Mar 2012
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Handle: RePEc:dgr:uvatin:20130050

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Web page: http://www.tinbergen.nl

Related research

Keywords: nonlinear non-Gaussian state space model; Bayesian inference; Monte Carlo estimation; Metropolis-Hastings algorithm; mixture of Student's t-distributions;

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