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Block Sampler and Posterior Mode Estimation for A Nonlinear and Non-Gaussian State-space Model with Correlated Errors

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  • Yasuhiro Omori

    (Faculty of Economics, University of Tokyo)

  • Toshiaki Watanabe

    (Institute of Economic Research, Hitotsubashi University)

Abstract

This article introduces a new efficient simulation smoother and disturbance smoother for general state-space models where there exists a correlation between error terms of the measurement and state equations. The state vector is divided into several blocks where each block consists of many state variables. For each block, corresponding disturbances are sampled simultaneously from their conditional posterior distribution. The algorithm is based on the multivariate normal approximation of the conditional posterior density and exploits a conventional simulation smoother for a linear and Gaussian state space model. The performance of our method is illustrated using two examples (1) stochastic volatility models with leverage effects and (2) stochastic volatility models with leverage effects and state-dependent variances. The popular single move sampler which samples a state variable at a time is also conducted for comparison in the first example. It is shown that our proposed sampler produces considerable improvement in the mixing property of the Markov chain Monte Carlo chain.

Suggested Citation

  • Yasuhiro Omori & Toshiaki Watanabe, 2007. "Block Sampler and Posterior Mode Estimation for A Nonlinear and Non-Gaussian State-space Model with Correlated Errors," CIRJE F-Series CIRJE-F-508, CIRJE, Faculty of Economics, University of Tokyo.
  • Handle: RePEc:tky:fseres:2007cf508
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    References listed on IDEAS

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    1. Sanford, Andrew D. & Martin, Gael M., 2005. "Simulation-based Bayesian estimation of an affine term structure model," Computational Statistics & Data Analysis, Elsevier, vol. 49(2), pages 527-554, April.
    2. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-370, March.
    3. J. Durbin & S. J. Koopman, 2000. "Time series analysis of non-Gaussian observations based on state space models from both classical and Bayesian perspectives," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(1), pages 3-56.
    4. Hisashi Tanizaki, 2001. "Nonlinear and Non-Gaussian State Space Modeling Using Sampling Techniques," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 53(1), pages 63-81, March.
    5. Harvey, Andrew C & Shephard, Neil, 1996. "Estimation of an Asymmetric Stochastic Volatility Model for Asset Returns," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(4), pages 429-434, October.
    6. 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.
    7. Andrew D. Sanford & Gael M. Martin, 2003. "Simulation-Based Bayesian Estimation of Affine Term Structure Models," Monash Econometrics and Business Statistics Working Papers 15/03, Monash University, Department of Econometrics and Business Statistics.
    8. Sangjoon Kim & Neil Shephard & Siddhartha Chib, 1998. "Stochastic Volatility: Likelihood Inference and Comparison with ARCH Models," Review of Economic Studies, Oxford University Press, vol. 65(3), pages 361-393.
    9. Fahrmeir, Ludwig & Wagenpfeil, Stefan, 1997. "Penalized likelihood estimation and iterative Kalman smoothing for non-Gaussian dynamic regression models," Computational Statistics & Data Analysis, Elsevier, vol. 24(3), pages 295-320, May.
    10. Jacquier, Eric & Polson, Nicholas G. & Rossi, P.E.Peter E., 2004. "Bayesian analysis of stochastic volatility models with fat-tails and correlated errors," Journal of Econometrics, Elsevier, vol. 122(1), pages 185-212, September.
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    Cited by:

    1. Omori, Yasuhiro & Watanabe, Toshiaki, 2008. "Block sampler and posterior mode estimation for asymmetric stochastic volatility models," Computational Statistics & Data Analysis, Elsevier, vol. 52(6), pages 2892-2910, February.

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