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Efficient high-dimensional importance sampling in mixture frameworks

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  • Kleppe, Tore Selland
  • Liesenfeld, Roman

Abstract

This paper provides high-dimensional and flexible importance sampling procedures for the likelihood evaluation of dynamic latent variable models involving finite or infinite mixtures leading to possibly heavy tailed and/or multi-modal target densities. Our approach is based upon the efficient importance sampling (EIS) approach of Richard and Zhang (2007) and exploits the mixture structure of the model when constructing importance sampling distributions as mixture of distributions. The proposed mixture EIS procedures are illustrated with ML estimation of a student-t state space model for realized volatilities and a stochastic volatility model with leverage effects and jumps for asset returns. --

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Bibliographic Info

Paper provided by Christian-Albrechts-University of Kiel, Department of Economics in its series Economics Working Papers with number 2011,11.

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Date of creation: 2011
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Handle: RePEc:zbw:cauewp:201111

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Related research

Keywords: dynamic latent variable model; importance sampling; marginalized likelihood; mixture; Monte Carlo; realized volatility; stochastic volatility;

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References

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  1. Sylvia Fr�Hwirth-Schnatter & Helga Wagner, 2006. "Auxiliary mixture sampling for parameter-driven models of time series of counts with applications to state space modelling," Biometrika, Biometrika Trust, Biometrika Trust, vol. 93(4), pages 827-841, December.
  2. Christian Bach & Bent Jesper Christensen, 2011. "Latent Integrated Stochastic Volatility, Realized Volatility, and Implied Volatility: A State Space Approach," CREATES Research Papers 2010-61, School of Economics and Management, University of Aarhus.
  3. Roxana Chiriac & Valeri Voev, 2008. "Modelling and Forecasting Multivariate Realized Volatility," CoFE Discussion Paper, Center of Finance and Econometrics, University of Konstanz 08-06, Center of Finance and Econometrics, University of Konstanz.
  4. David Ardia & Lennart F. Hoogerheide & Herman K. van Dijk, . "Adaptive Mixture of Student-t Distributions as a Flexible Candidate Distribution for Efficient Simulation: The R Package AdMit," Journal of Statistical Software, American Statistical Association, American Statistical Association, vol. 29(i03).
  5. Ole E. Barndorff-Nielsen & Neil Shephard, 2000. "Econometric analysis of realised volatility and its use in estimating stochastic volatility models," Economics Papers 2001-W4, Economics Group, Nuffield College, University of Oxford, revised 05 Jul 2001.
  6. BAUWENS, Luc & GALLI, Fausto, . "Efficient importance sampling for ML estimation of SCD models," CORE Discussion Papers RP, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) -2088, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  7. Durham, Garland B., 2006. "Monte Carlo methods for estimating, smoothing, and filtering one- and two-factor stochastic volatility models," Journal of Econometrics, Elsevier, Elsevier, vol. 133(1), pages 273-305, July.
  8. Jung, Robert C. & Liesenfeld, Roman & Richard, Jean-François, 2011. "Dynamic Factor Models for Multivariate Count Data: An Application to Stock-Market Trading Activity," Journal of Business & Economic Statistics, American Statistical Association, American Statistical Association, vol. 29(1), pages 73-85.
  9. Richard, Jean-Francois & Zhang, Wei, 2007. "Efficient high-dimensional importance sampling," Journal of Econometrics, Elsevier, Elsevier, vol. 141(2), pages 1385-1411, December.
  10. Cox, John C & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1985. "A Theory of the Term Structure of Interest Rates," Econometrica, Econometric Society, Econometric Society, vol. 53(2), pages 385-407, March.
  11. Jun Yu, 2004. "On Leverage in a Stochastic Volatility Model," Working Papers, Singapore Management University, School of Economics 13-2004, Singapore Management University, School of Economics.
  12. Liesenfeld, Roman & Richard, Jean-François, 2010. "Efficient estimation of probit models with correlated errors," Journal of Econometrics, Elsevier, Elsevier, vol. 156(2), pages 367-376, June.
  13. Bjørn Eraker & Michael Johannes & Nicholas Polson, 2003. "The Impact of Jumps in Volatility and Returns," Journal of Finance, American Finance Association, American Finance Association, vol. 58(3), pages 1269-1300, 06.
  14. Liesenfeld, Roman & Richard, Jean-Francois, 2003. "Univariate and multivariate stochastic volatility models: estimation and diagnostics," Journal of Empirical Finance, Elsevier, Elsevier, vol. 10(4), pages 505-531, September.
  15. Geweke, John, 1989. "Bayesian Inference in Econometric Models Using Monte Carlo Integration," Econometrica, Econometric Society, Econometric Society, vol. 57(6), pages 1317-39, November.
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Cited by:
  1. Tore Selland Kleppe & Jun Yu & Hans J. skaug, 2011. "Simulated Maximum Likelihood Estimation for Latent Diffusion Models," Working Papers, Singapore Management University, School of Economics 10-2011, Singapore Management University, School of Economics.

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