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Adaptive polar sampling with an application to a Bayes measure of value-at-risk

Author

Listed:
  • BAUWENS, Luc

    () (Center for Operations Research and Econometrics (CORE), Université catholique de Louvain (UCL), Louvain la Neuve, Belgium)

  • BOS, Charles S.

    () (Econometric and Tinbergen Institutes, Erasmus University Rotterdam, P.O.Box 1738, NL-3000 DR Rotterdam, The Netherlands)

  • VAN DIJK, Herman K.

    () (Econometric Institute, Erasmus University Rotterdam)

Abstract

Adaptive Polar Sampling (APS) is proposed as a Markov chain Monte Carlo method for Bayesian analysis of models with ill-behaved posterior distributions. In order to sample efficiently from such a distribution, location-scale transformation and a transformation to polar coordinates are used. After the transformation to polar coordinates, a MetropolisHastings algorithm is applied to sample directions and, conditionally on these, distances are generated by inverting the CDF. A sequential procedure is applied to update the location and scale. Tested on a set of canonical models that feature near non-identifiability, strong correlation, and bimodality, APS compares favourably with the standard Metropolis-Hastings sampler in terms of parsimony and robustness. APS is applied within a Bayesian analysis of a GARCH-mixture model which is used for the evaluation of the Value-at-Risk of the return of the Dow Jones stock index.

Suggested Citation

  • BAUWENS, Luc & BOS, Charles S. & VAN DIJK, Herman K., 1999. "Adaptive polar sampling with an application to a Bayes measure of value-at-risk," CORE Discussion Papers 1999057, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  • Handle: RePEc:cor:louvco:1999057
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    File URL: https://uclouvain.be/en/research-institutes/immaq/core/dp-1999.html
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Mohamed Saidane & Christian Lavergne, 2009. "Optimal Prediction with Conditionally Heteroskedastic Factor Analysed Hidden Markov Models," Computational Economics, Springer;Society for Computational Economics, vol. 34(4), pages 323-364, November.
    2. Dinghai Xu, 2009. "The Applications of Mixtures of Normal Distributions in Empirical Finance: A Selected Survey," Working Papers 0904, University of Waterloo, Department of Economics, revised Sep 2009.
    3. Dinghai Xu & Tony S. Wirjanto, 2008. "An Empirical Characteristic Function Approach to VaR under a Mixture of Normal Distribution with Time-Varying Volatility," Working Papers 08008, University of Waterloo, Department of Economics.
    4. Emese Lazar & Carol Alexander, 2006. "Normal mixture GARCH(1,1): applications to exchange rate modelling," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(3), pages 307-336.
    5. BAUWENS, Luc & PREMINGER, Arie & ROMBOUTS, Jeroen, 2006. "Regime switching GARCH models," CORE Discussion Papers 2006011, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).

    More about this item

    Keywords

    Markov chain Monte Carlo; simulation; polar coordinates; GARCH; ill-behaved posterior; Value-at-Risk.;

    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
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques

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