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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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Author Info

  • Yasuhiro Omori

    (Faculty of Economics, The University of Tokyo)

  • Toshiaki Watanabe

    (Faculty of Economics, Tokyo Metropolitan University)

Abstract

In a linear Gaussian state-space time series analysis, a disturbance smoother and a simula-tion smoother are widely used procedures for smoothing and sampling state or disturbance vectors given observations. Several smoothing procedures are also proposed for a non-Gaussian observation process. However, it is assumed that a state equation is linear and that an observation vector and a state vector are conditionally independent. These as-sumptions often need to be relaxed in the analysis of real data. Thus this article considers a general state-space model with a non-Gaussian observation process and a nonlinear state equation where an observation vector and a state vector are allowed to be dependent. We describe a disturbance smoother and a simulation smoother for such models and give numerical examples using simulated data and real data.

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Bibliographic Info

Paper provided by CIRJE, Faculty of Economics, University of Tokyo in its series CIRJE F-Series with number CIRJE-F-221.

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Length: 40 pages
Date of creation: May 2003
Date of revision:
Handle: RePEc:tky:fseres:2003cf221

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  1. 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.
  2. Durbin, J. & Koopman, S.J.M., 1998. "Time Series Analysis of Non-Gaussian Observations Based on State Space Models from Both Classical and Bayesian Perspectives," Discussion Paper 1998-142, Tilburg University, Center for Economic Research.
  3. Kim, Sangjoon & Shephard, Neil & Chib, Siddhartha, 1998. "Stochastic Volatility: Likelihood Inference and Comparison with ARCH Models," Review of Economic Studies, Wiley Blackwell, vol. 65(3), pages 361-93, July.
  4. 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 429-34, October.
  5. Hisashi Tanizaki, 2001. "Nonlinear and Non-Gaussian State Space Modeling Using Sampling Techniques," Annals of the Institute of Statistical Mathematics, Springer, vol. 53(1), pages 63-81, March.
  6. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-70, March.
  7. 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.
  8. 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.
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