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Adaptive Mixture of Student-t Distributions as a Flexible Candidate Distribution for Efficient Simulation: The R Package AdMit

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  • Ardia, David
  • Hoogerheide, Lennart F.
  • van Dijk, Herman K.

Abstract

This paper presents the R package AdMit which provides flexible functions to approximate a certain target distribution and to efficiently generate a sample of random draws from it, given only a kernel of the target density function. The core algorithm consists of the function AdMit which fits an adaptive mixture of Student-t distributions to the density of interest. Then, importance sampling or the independence chain Metropolis-Hastings algorithm is 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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  • 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).
  • Handle: RePEc:jss:jstsof:v:029:i03
    DOI: http://hdl.handle.net/10.18637/jss.v029.i03
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    1. Hoogerheide, Lennart & van Dijk, Herman K., 2010. "Bayesian forecasting of Value at Risk and Expected Shortfall using adaptive importance sampling," International Journal of Forecasting, Elsevier, vol. 26(2), pages 231-247, April.
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    3. 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.
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    7. 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.
    8. Geweke, John, 2007. "Interpretation and inference in mixture models: Simple MCMC works," Computational Statistics & Data Analysis, Elsevier, vol. 51(7), pages 3529-3550, April.
    9. 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, Decembrie.
    10. 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.
    11. David, D. & Hoogerheide, L.F. & van Dijk, H.K., 2008. "The AdMit Package," Econometric Institute Research Papers EI 2008-17, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    12. 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 225-234, April.
    13. David Ardia, 2008. "Financial Risk Management with Bayesian Estimation of GARCH Models," Lecture Notes in Economics and Mathematical Systems, Springer, number 978-3-540-78657-3, October.
    14. 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.
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    Cited by:

    1. Natalia Khorunzhina & Jean-François Richard, 2019. "Finite Gaussian Mixture Approximations to Analytically Intractable Density Kernels," Computational Economics, Springer;Society for Computational Economics, vol. 53(3), pages 991-1017, March.
    2. 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.
    3. Ardia, David & Baştürk, Nalan & Hoogerheide, Lennart & van Dijk, Herman K., 2012. "A comparative study of Monte Carlo methods for efficient evaluation of marginal likelihood," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3398-3414.
    4. Ardia, David & Hoogerheide, Lennart F., 2010. "Efficient Bayesian estimation and combination of GARCH-type models," MPRA Paper 22919, University Library of Munich, Germany.
    5. Baştürk, Nalan & Grassi, Stefano & Hoogerheide, Lennart & Opschoor, Anne & van Dijk, Herman K., 2017. "The R Package MitISEM: Efficient and Robust Simulation Procedures for Bayesian Inference," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 79(i01).
    6. Kleppe, Tore Selland & Liesenfeld, Roman, 2014. "Efficient importance sampling in mixture frameworks," Computational Statistics & Data Analysis, Elsevier, vol. 76(C), pages 449-463.
    7. Hautsch, Nikolaus & Yang, Fuyu, 2012. "Bayesian inference in a Stochastic Volatility Nelson–Siegel model," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3774-3792.
    8. 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).
    9. Ardia, David & Bluteau, Keven & Boudt, Kris & Catania, Leopoldo, 2018. "Forecasting risk with Markov-switching GARCH models:A large-scale performance study," International Journal of Forecasting, Elsevier, vol. 34(4), pages 733-747.
    10. Olofsson, Petter & Råholm, Anna & Uddin, Gazi Salah & Troster, Victor & Kang, Sang Hoon, 2021. "Ethical and unethical investments under extreme market conditions," International Review of Financial Analysis, Elsevier, vol. 78(C).
    11. David Ardia & Lennart Hoogerheide & Herman K. van Dijk, 2009. "To Bridge, to Warp or to Wrap? A Comparative Study of Monte Carlo Methods for Efficient Evaluation of Marginal Likelihoods," Tinbergen Institute Discussion Papers 09-017/4, Tinbergen Institute.
    12. Geweke, John & Durham, Garland, 2019. "Sequentially adaptive Bayesian learning algorithms for inference and optimization," Journal of Econometrics, Elsevier, vol. 210(1), pages 4-25.

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    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General

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