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An effcient exact Bayesian method For state space models with stochastic volatility

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  • Huang Yu-Fan

    (Capital University of Economics and Business, International School of Economics and Management, 121 Zhangjialukou, Huaxiang Fengtai District, Beijing, China)

Abstract

This paper introduces a Bayesian MCMC method, referred to as a marginalized mixture sampler, for state space models whose disturbances follow stochastic volatility processes. The marginalized mixture sampler is based on a mixture-normal approximation of the log-χ 2 distribution, but it is implemented without the need to simulate the mixture indicator variable. The key innovation is to use the filter ing scheme developed by Kim (Kim C.-J. 1994. “Dynamic Linear Models with Markov-Switching.” Journal of Econometrics 60: 1–22.) and the forward-filtering backward-sampling algorithm to generate a proposal series of the latent stochastic volatility process. The proposal series is then accepted according to the Metropolis-Hastings acceptance probability. The new sampler is examined within an unobserved component model and a time-varying parameter vector autoregressive model, and it reduces substantially the correlations between MCMC draws.

Suggested Citation

  • Huang Yu-Fan, 2021. "An effcient exact Bayesian method For state space models with stochastic volatility," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 25(2), pages 1-10, April.
    • Handle: RePEc:bpj:sndecm:v:25:y:2021:i:2:p:10:n:6
    DOI: 10.1515/snde-2018-0098
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    References listed on IDEAS

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    1. Sangjoon Kim & Neil Shephard & Siddhartha Chib, 1998. "Stochastic Volatility: Likelihood Inference and Comparison with ARCH Models," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 65(3), pages 361-393.
    2. James C. Morley & Charles R. Nelson & Eric Zivot, 2003. "Why Are the Beveridge-Nelson and Unobserved-Components Decompositions of GDP So Different?," The Review of Economics and Statistics, MIT Press, vol. 85(2), pages 235-243, May.
    3. Charles Bos & Neil Shephard, 2006. "Inference for Adaptive Time Series Models: Stochastic Volatility and Conditionally Gaussian State Space Form," Econometric Reviews, Taylor & Francis Journals, vol. 25(2-3), pages 219-244.
    4. Kim, Chang-Jin, 1994. "Dynamic linear models with Markov-switching," Journal of Econometrics, Elsevier, vol. 60(1-2), pages 1-22.
    5. Giordani, Paolo & Kohn, Robert, 2008. "Efficient Bayesian Inference for Multiple Change-Point and Mixture Innovation Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 26, pages 66-77, January.
    6. Giorgio E. Primiceri, 2005. "Time Varying Structural Vector Autoregressions and Monetary Policy," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 72(3), pages 821-852.
    7. Marco Del Negro & Giorgio E. Primiceri, 2015. "Time Varying Structural Vector Autoregressions and Monetary Policy: A Corrigendum," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 82(4), pages 1342-1345.
    8. Omori, Yasuhiro & Chib, Siddhartha & Shephard, Neil & Nakajima, Jouchi, 2007. "Stochastic volatility with leverage: Fast and efficient likelihood inference," Journal of Econometrics, Elsevier, vol. 140(2), pages 425-449, October.
    9. J. Durbin, 2002. "A simple and efficient simulation smoother for state space time series analysis," Biometrika, Biometrika Trust, vol. 89(3), pages 603-616, August.
    10. Chang-Jin Kim & Charles R. Nelson, 1999. "State-Space Models with Regime Switching: Classical and Gibbs-Sampling Approaches with Applications," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262112388, December.
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