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Adaptive Mixture of Student-t distributions as a Flexible Candidate Distribution for Efficient Simulation

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Author Info

  • David Ardia

    ()
    (University of Fribourg)

  • Lennart F. Hoogerheide

    ()
    (Erasmus University Rotterdam)

  • Herman K. van Dijk

    ()
    (Erasmus University Rotterdam)

Abstract

This paper presents the R package AdMit which provides functions to approximate and sample from a certain target distribution given only a kernel of the target density function. The core algorithm consists in the function AdMit which fits an adaptive mixture of Student-t distributions to the density of interest via its kernel function. Then, importance sampling or the independence chain Metropolis- Hastings algorithm are used to obtain quantities of interest for the target density, using the fitted mixture as the importance or candidate density. The estimation procedure is fully automatic and thus avoids the time-consuming and difficult task of tuning a sampling algorithm. The relevance of the package is shown in two examples. The first aims at illustrating in detail the use of the functions provided by the package in a bivariate bimodal distribution. The second shows the relevance of the adaptive mixture procedure through the Bayesian estimation of a mixture of ARCH model fitted to foreign exchange log-returns data. The methodology is compared to standard cases of importance sampling and the Metropolis-Hastings algorithm using a naive candidate and with the Griddy-Gibbs approach.

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File URL: http://papers.tinbergen.nl/08062.pdf
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Bibliographic Info

Paper provided by Tinbergen Institute in its series Tinbergen Institute Discussion Papers with number 08-062/4.

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Date of creation: 18 Jun 2008
Date of revision: 15 Dec 2008
Handle: RePEc:dgr:uvatin:20080062

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Web page: http://www.tinbergen.nl

Related research

Keywords: adaptive mixture; Student-t distributions; importance sampling; independence chain Metropolis-Hasting algorithm; Bayesian; R software;

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References

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  1. Hoogerheide, Lennart F. & Kaashoek, Johan F. & van Dijk, Herman K., 2007. "On the shape of posterior densities and credible sets in instrumental variable regression models with reduced rank: An application of flexible sampling methods using neural networks," Journal of Econometrics, Elsevier, vol. 139(1), pages 154-180, July.
  2. 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.
  3. Bollerslev, T. & Ghysels, E., 1994. "Periodic Autoregressive Conditional Heteroskedasticity," Cahiers de recherche 9408, Universite de Montreal, Departement de sciences economiques.
  4. Marcucci Juri, 2005. "Forecasting Stock Market Volatility with Regime-Switching GARCH Models," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 9(4), pages 1-55, December.
  5. Heij, Christiaan & de Boer, Paul & Franses, Philip Hans & Kloek, Teun & van Dijk, Herman K., 2004. "Econometric Methods with Applications in Business and Economics," OUP Catalogue, Oxford University Press, number 9780199268016.
  6. Lennart Hoogerheide & Herman K. van Dijk, 2008. "Bayesian Forecasting of Value at Risk and Expected Shortfall using Adaptive Importance Sampling," Tinbergen Institute Discussion Papers 08-092/4, Tinbergen Institute.
  7. Lamoureux, Christopher G & Lastrapes, William D, 1990. "Persistence in Variance, Structural Change, and the GARCH Model," Journal of Business & Economic Statistics, American Statistical Association, vol. 8(2), pages 225-34, April.
  8. Lennart Hoogerheide & Herman K. van Dijk, 2008. "Possibly Ill-behaved Posteriors in Econometric Models," Tinbergen Institute Discussion Papers 08-036/4, Tinbergen Institute, revised 18 Apr 2008.
  9. Geweke, John, 2007. "Interpretation and inference in mixture models: Simple MCMC works," Computational Statistics & Data Analysis, Elsevier, vol. 51(7), pages 3529-3550, April.
  10. Ardia, David & Hoogerheide, Lennart F. & van Dijk, Herman K., 2008. "AdMit: Adaptive Mixtures of Student-t Distributions," DQE Working Papers 10, Department of Quantitative Economics, University of Freiburg/Fribourg Switzerland, revised 07 Jan 2009.
  11. Sylvia Frühwirth-Schnatter, 2001. "Fully Bayesian Analysis of Switching Gaussian State Space Models," Annals of the Institute of Statistical Mathematics, Springer, vol. 53(1), pages 31-49, March.
  12. Franc Klaassen, 2002. "Improving GARCH volatility forecasts with regime-switching GARCH," Empirical Economics, Springer, vol. 27(2), pages 363-394.
  13. Geweke, John, 1989. "Bayesian Inference in Econometric Models Using Monte Carlo Integration," Econometrica, Econometric Society, vol. 57(6), pages 1317-39, November.
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Cited by:
  1. David Ardia & Nalan Basturk & Lennart Hoogerheide & Herman K. van Dijk, 2010. "A Comparative Study of Monte Carlo Methods for Efficient Evaluation of Marginal Likelihoods," Tinbergen Institute Discussion Papers 10-059/4, Tinbergen Institute.
  2. David Ardia & Lennart F. Hoogerheide, 2010. "Efficient Bayesian Estimation and Combination of GARCH-Type Models," Tinbergen Institute Discussion Papers 10-046/4, Tinbergen Institute.

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