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Improving MCMC Using Efficient Importance Sampling

  • Liesenfeld, Roman
  • Richard, Jean-François

This paper develops a systematic Markov Chain Monte Carlo (MCMC) framework based upon Efficient Importance Sampling (EIS) which can be used for the analysis of a wide range of econometric models involving integrals without an analytical solution. EIS is a simple, generic and yet accurate Monte-Carlo integration procedure based on sampling densities which are chosen to be global approximations to the integrand. By embedding EIS within MCMC procedures based on Metropolis-Hastings (MH) one can significantly improve their numerical properties, essentially by providing a fully automated selection of critical MCMC components such as auxiliary sampling densities, normalizing constants and starting values. The potential of this integrated MCMC- EIS approach is illustrated with simple univariate integration problems and with the Bayesian posterior analysis of stochastic volatility models and stationary autoregressive processes.

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Paper provided by Christian-Albrechts-University of Kiel, Department of Economics in its series Economics Working Papers with number 2006,05.

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Date of creation: 2006
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Handle: RePEc:zbw:cauewp:4349
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  1. Ghysels, E. & Harvey, A. & Renault, E., 1996. "Stochastic Volatility," Cahiers de recherche 9613, Universite de Montreal, Departement de sciences economiques.
  2. repec:zbw:cauewp:2443 is not listed on IDEAS
  3. BAUWENS, Luc & HAUTSCH, Nikolaus, . "Stochastic conditional intensity processes," CORE Discussion Papers RP 1937, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  4. Geweke, John, 1989. "Bayesian Inference in Econometric Models Using Monte Carlo Integration," Econometrica, Econometric Society, vol. 57(6), pages 1317-39, November.
  5. Jean-Francois Richard & Roman Liesenfeld, 2007. "Classical and Bayesian Analysis of Univariate and Multivariate Stochastic Volatility Models," Working Papers 322, University of Pittsburgh, Department of Economics, revised Jan 2004.
  6. Siem Jan Koopman & Neil Shephard, 2002. "Testing the Assumptions Behind the Use of Importance Sampling," Economics Papers 2002-W17, Economics Group, Nuffield College, University of Oxford.
  7. Jacquier, Eric & Polson, Nicholas G & Rossi, Peter E, 1994. "Bayesian Analysis of Stochastic Volatility Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(4), pages 371-89, October.
  8. Sangjoon Kim & Neil Shephard & Siddhartha Chib, 1996. "Stochastic Volatility: Likelihood Inference And Comparison With Arch Models," Econometrics 9610002, EconWPA.
  9. Liesenfeld, Roman & Richard, Jean-Francois, 2003. "Estimation of Dynamic Bivariate Mixture Models: Comments on Watanabe (2000)," Journal of Business & Economic Statistics, American Statistical Association, vol. 21(4), pages 570-76, October.
  10. Shephard, N. & Pitt, M.K., 1995. "Likelihood Analysis of Non-Gaussian Parameter-Driven Models," Economics Papers 108, Economics Group, Nuffield College, University of Oxford.
  11. Neil Shephard, 2005. "Stochastic volatility," Economics Series Working Papers 2005-W17, University of Oxford, Department of Economics.
  12. Kloek, Tuen & van Dijk, Herman K, 1978. "Bayesian Estimates of Equation System Parameters: An Application of Integration by Monte Carlo," Econometrica, Econometric Society, vol. 46(1), pages 1-19, January.
  13. BAUWENS, Luc & HAUTSCH, Nikolaus, 2003. "Dynamic latent factor models for intensity processes," CORE Discussion Papers 2003103, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  14. Sandmann, Gleb & Koopman, Siem Jan, 1998. "Estimation of stochastic volatility models via Monte Carlo maximum likelihood," Journal of Econometrics, Elsevier, vol. 87(2), pages 271-301, September.
  15. Jean-Francois Richard, 2007. "Efficient High-Dimensional Importance Sampling," Working Papers 321, University of Pittsburgh, Department of Economics, revised Jan 2007.
  16. Chib, Siddhartha & Greenberg, Edward, 1994. "Bayes inference in regression models with ARMA (p, q) errors," Journal of Econometrics, Elsevier, vol. 64(1-2), pages 183-206.
  17. Chib, Siddhartha & Nardari, Federico & Shephard, Neil, 2002. "Markov chain Monte Carlo methods for stochastic volatility models," Journal of Econometrics, Elsevier, vol. 108(2), pages 281-316, June.
  18. John Geweke, 1999. "Using simulation methods for bayesian econometric models: inference, development,and communication," Econometric Reviews, Taylor & Francis Journals, vol. 18(1), pages 1-73.
  19. Liesenfeld, Roman & Richard, Jean-Francois, 2003. "Univariate and multivariate stochastic volatility models: estimation and diagnostics," Journal of Empirical Finance, Elsevier, vol. 10(4), pages 505-531, September.
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