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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.

Suggested Citation

  • Kleppe, Tore Selland & Liesenfeld, Roman, 2011. "Efficient high-dimensional importance sampling in mixture frameworks," Economics Working Papers 2011-11, Christian-Albrechts-University of Kiel, Department of Economics.
    • Handle: RePEc:zbw:cauewp:201111
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    References listed on IDEAS

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    1. 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, vol. 29(1), pages 73-85.
    2. Geweke, John, 1989. "Bayesian Inference in Econometric Models Using Monte Carlo Integration," Econometrica, Econometric Society, vol. 57(6), pages 1317-1339, November.
    3. Robert C. Jung & Roman Liesenfeld & Jean-François Richard, 2011. "Dynamic Factor Models for Multivariate Count Data: An Application to Stock-Market Trading Activity," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 29(1), pages 73-85, January.
    4. 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.
    5. John C. Cox & Jonathan E. Ingersoll Jr. & Stephen A. Ross, 2005. "A Theory Of The Term Structure Of Interest Rates," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 5, pages 129-164, World Scientific Publishing Co. Pte. Ltd..
    6. Bauwens, L. & Galli, F., 2009. "Efficient importance sampling for ML estimation of SCD models," Computational Statistics & Data Analysis, Elsevier, vol. 53(6), pages 1974-1992, April.
    7. Roxana Chiriac & Valeri Voev, 2011. "Modelling and forecasting multivariate realized volatility," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 26(6), pages 922-947, September.
    8. Christian Bach & Bent Jesper Christensen, 2011. "Latent Integrated Stochastic Volatility, Realized Volatility, and Implied Volatility: A State Space Approach," CREATES Research Papers 2010-61, Department of Economics and Business Economics, Aarhus University.
    9. Sylvia FrüHwirth-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, vol. 93(4), pages 827-841, December.
    10. 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.
    11. Ole E. Barndorff‐Nielsen & Neil Shephard, 2002. "Econometric analysis of realized volatility and its use in estimating stochastic volatility models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(2), pages 253-280, May.
    12. Yu, Jun, 2005. "On leverage in a stochastic volatility model," Journal of Econometrics, Elsevier, vol. 127(2), pages 165-178, August.
    13. Malik, S. & Pitt, M. K., 2011. "Modelling Stochastic Volatility with Leverage and Jumps: A Simulated Maximum Likelihood Approach via Particle Filtering," Working papers 318, Banque de France.
    14. Liesenfeld, Roman & Richard, Jean-François, 2010. "Efficient estimation of probit models with correlated errors," Journal of Econometrics, Elsevier, vol. 156(2), pages 367-376, June.
    15. Durham, Garland B., 2006. "Monte Carlo methods for estimating, smoothing, and filtering one- and two-factor stochastic volatility models," Journal of Econometrics, Elsevier, vol. 133(1), pages 273-305, July.
    16. Bjørn Eraker & Michael Johannes & Nicholas Polson, 2003. "The Impact of Jumps in Volatility and Returns," Journal of Finance, American Finance Association, vol. 58(3), pages 1269-1300, June.
    17. Geweke, J, 1993. "Bayesian Treatment of the Independent Student- t Linear Model," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 8(S), pages 19-40, Suppl. De.
    18. Ardia, David & Hoogerheide, Lennart F. & van Dijk, Herman K., 2009. "Adaptive Mixture of Student-t Distributions as a Flexible Candidate Distribution for Efficient Simulation: The R Package AdMit," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 29(i03).
    19. Richard, Jean-Francois & Zhang, Wei, 2007. "Efficient high-dimensional importance sampling," Journal of Econometrics, Elsevier, vol. 141(2), pages 1385-1411, December.
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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 CoFie-04-2011, Singapore Management University, Sim Kee Boon Institute for Financial Economics.
    2. Kleppe, Tore Selland & Yu, Jun & Skaug, Hans J., 2014. "Maximum likelihood estimation of partially observed diffusion models," Journal of Econometrics, Elsevier, vol. 180(1), pages 73-80.

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    More about this item

    Keywords

    dynamic latent variable model; importance sampling; marginalized likelihood; mixture; Monte Carlo; realized volatility; stochastic volatility;
    All these keywords.

    JEL classification:

    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General

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