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

and Yu-Fan Huang
  • Corresponding author
  • Capital University of Economics and Business, International School of Economics and Management, 121 Zhangjialukou, Huaxiang Fengtai District, Beijing, China
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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-χ2 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.

    • Supplementary Material
  • Bos, C. S., and N. Shephard. 2006. “Inference for Adaptive Time Series Models: Stochastic Volatility and Conditionally Gaussian State Space Form.” Econometric Reviews 25: 219–244.

  • Carter, C. K., and R. J. Kohn. 1994. “On Gibbs Sampling for State Space Models.” Biometrika 81: 541–553.

  • Carter, C. K., and R. J. Kohn. 1996. “Markov Chain Monte Carlo in Conditionally Gaussian State Space Models.” Biometrika 83: 589–601.

  • Chib, S. 2011. “Introduction to Simulation and MCMC Methods.” In The Oxford Handbook of Bayesian Econometrics, edited by J. Geweke, G. Koop, and H. van Dijk. Oxford, UK: Oxford University Press.

  • Del Negro, M., and G. E. Primiceri. 2015. “Time Varying Structural Vector Autoregressions and Monetary Policy: A Corrigendum.” Review of Economic Studies 82: 1342–1345.

  • Durbin, J., and S. J. Koopman. 2002. “A Simple and Efficient Simulation Smoother for State Space Time Series Analysis.” Biometrika 89: 603–615.

  • Frühwirth-Schnatter, S. 2006. Finite Mixture and Markov Switching Models. Berlin, German: Springer Science & Business Media.

  • Giordani, P., and R. Kohn. 2008. “Efficient Bayesian Inference for Multiple Change-Point and Mixture Innovation Models.” Journal of Business & Economic Statistics 26: 66–77.

  • Giordani, P., M. Pitt, and R. Kohn. 2011. “Bayesian Inference for Time Series State Space Models.” In The Oxford Handbook of Bayesian Econometrics, edited by J. Geweke, G. Koop, and H. van Dijk. Oxford, UK: Oxford University Press.

  • Huber, F., G. Kastner, and M. Feldkircher. 2019. “Should I Stay or should I Go? A Latent Threshold Approach to Large-Scale Mixture Innovation Models.” Journal of Applied Econometrics 34: 621–640.

  • Kastner, G. 2019. “Sparse Bayesian Time-Varying Covariance Estimation in Many Dimensions.” Journal of Econometrics 210: 98–115.

  • Kastner, G., and S. Frühwirth-Schnatter. 2014. “Ancillarity-Sufficiency Interweaving Strategy (Asis) for Boosting MCMC Estimation of Stochastic Volatility Models.” Computational Statistics & Data Analysis 76: 408–423.

  • Kim, C.-J. 1994. “Dynamic Linear Models with Markov-Switching.” Journal of Econometrics 60: 1–22.

  • Kim, C.-J., and C. R. Nelson. 1999. State-Space Models with Regime Switching: Classical and Gibbs-Sampling Approaches with Applications. Cambridge, US: The MIT Press.

  • Kim, S., N. Shephard, and S. Chib. 1998. “Stochastic Volatility: Likelihood Inference and Comparison with Arch Models.” Review of Economic Studies 65: 361–93.

  • Koop, G. 2003. Bayesian Econometrics. Hoboken, US: John Wiley & Son.

  • Koop, G., R. Leon-Gonzalez, and R. W. Strachan. 2009. “On the Evolution of the Monetary Policy Transmission Mechanism.” Journal of Economic Dynamics and Control 33: 997–1017.

  • Morley, J. C., C. R. Nelson, and E. Zivot. 2003. “Why are the Beveridge-Nelson and Unobserved-Components Decompositions of GDP so Different?” The Review of Economics and Statistics 85: 235–243.

  • Omori, Y., S. Chib, N. Shephard, and J. Nakajima. 2007. “Stochastic Volatility with Leverage: Fast and Efficient Likelihood Inference.” Journal of Econometrics 140: 425–449.

  • Primiceri, G. E. 2005. “Time Varying Structural Vector Autoregressions and Monetary Policy.” The Review of Economic Studies 72: 821–852.

  • Shephard, N., and M. K. Pitt. 1997. “Likelihood Analysis of Non-Gaussian Measurement Time Series.” Biometrika 84: 653–667.

  • Stroud, J. R., P. Müller, and N. G. Polson. 2003. “Nonlinear State-Space Models with State-Dependent Variances.” Journal of the American Statistical Association 98: 377–386.

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SNDE recognizes that advances in statistics and dynamical systems theory can increase our understanding of economic and financial markets. The journal seeks both theoretical and applied papers that characterize and motivate nonlinear phenomena. Researchers are required to assist replication of empirical results by providing copies of data and programs online. Algorithms and rapid communications are also published.

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