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Adaptive Polar Sampling With An Application To A Bayes Measure Of Value-At-Risk

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Author Info
K. Van Dijk (Erasmus University of Rotterdam)
Luc Bauwens (CORE, Belgium)
Charles Bos (Erasmus University Rotterdam)

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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, a location-scale transformation and a transformation to polar coordinates are used. After the transformation to polar coordinates, a Metropolis-Hastings 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 aGARCH-mixture model which is used for the evaluation of the Value-at-Risk of the return of the Dow Jones stock index.

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Publisher Info
Paper provided by Society for Computational Economics in its series Computing in Economics and Finance 2000 with number 145.

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Date of creation: 05 Jul 2000
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Handle: RePEc:sce:scecf0:145

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Postal: CEF 2000, Departament d'Economia i Empresa, Universitat Pompeu Fabra, Ramon Trias Fargas, 25,27, 08005, Barcelona, Spain
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Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. van Dijk, H. K. & Kloek, T., 1980. "Further experience in Bayesian analysis using Monte Carlo integration," Journal of Econometrics, Elsevier, vol. 14(3), pages 307-328, December. [Downloadable!] (restricted)
  2. John Geweke, 1998. "Using simulation methods for Bayesian econometric models: inference, development, and communication," Staff Report 249, Federal Reserve Bank of Minneapolis. [Downloadable!]
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  3. Richard Paap & Herman K. van Dijk, 1999. "Bayes Estimates of Markov Trends in Possibly Cointegrated Series: An Application to US Consumption and Income," Tinbergen Institute Discussion Papers 99-024/4, Tinbergen Institute. [Downloadable!]
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  4. Kleibergen, F & Van Dijk, H K, 1993. "Non-stationarity in GARCH Models: A Bayesian Analysis," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 8(S), pages S41-61, Suppl. De. [Downloadable!] (restricted)
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  5. Kleibergen, Frank & van Dijk, Herman K., 1998. "Bayesian Simultaneous Equations Analysis Using Reduced Rank Structures," Econometric Theory, Cambridge University Press, vol. 14(06), pages 701-743, December. [Downloadable!]
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  6. repec:cup:etheor:v:10:y:1994:i:3-4:p:514-51 is not listed on IDEAS
  7. Kleibergen, Frank & van Dijk, Herman K., 1994. "On the Shape of the Likelihood/Posterior in Cointegration Models," Econometric Theory, Cambridge University Press, vol. 10(3-4), pages 514-551, August. [Downloadable!]
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  8. Albert, James H & Chib, Siddhartha, 1993. "Bayes Inference via Gibbs Sampling of Autoregressive Time Series Subject to Markov Mean and Variance Shifts," Journal of Business & Economic Statistics, American Statistical Association, vol. 11(1), pages 1-15, January.
  9. Luc Bauwens & Michel Lubrano, 1998. "Bayesian inference on GARCH models using the Gibbs sampler," Econometrics Journal, Royal Economic Society, vol. 1(Conferenc), pages C23-C46.
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  10. John Geweke, 1991. "Evaluating the accuracy of sampling-based approaches to the calculation of posterior moments," Staff Report 148, Federal Reserve Bank of Minneapolis. [Downloadable!]
  11. Frank Kleibergen & Herman K. van Dijk, 1998. "Bayesian Simultaneous Equations Analysis using Reduced Rank Structures," Tinbergen Institute Discussion Papers 98-025/4, Tinbergen Institute. [Downloadable!]
  12. Van Dijk, Herman K. & Kloek, Teun & Boender, C. Guus E., 1985. "Posterior moments computed by mixed integration," Journal of Econometrics, Elsevier, vol. 29(1-2), pages 3-18. [Downloadable!] (restricted)
  13. Chib, Siddhartha & Greenberg, Edward, 1996. "Markov Chain Monte Carlo Simulation Methods in Econometrics," Econometric Theory, Cambridge University Press, vol. 12(03), pages 409-431, August. [Downloadable!]
  14. Geweke, John, 1989. "Exact predictive densities for linear models with arch disturbances," Journal of Econometrics, Elsevier, vol. 40(1), pages 63-86, January. [Downloadable!] (restricted)
  15. G. Koop & H.K. van Dijk, 1999. "Testing for integration using evolving trend and seasonal models A Bayesian approach," Econometric Institute Report 163, Erasmus University Rotterdam, Econometric Institute. [Downloadable!]
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  16. repec:cup:etheor:v:12:y:1996:i:3:p:409-31 is not listed on IDEAS
  17. Kim, Sangjoon & Shephard, Neil & Chib, Siddhartha, 1998. "Stochastic Volatility: Likelihood Inference and Comparison with ARCH Models," Review of Economic Studies, Blackwell Publishing, vol. 65(3), pages 361-93, July. [Downloadable!] (restricted)
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  18. Geweke, J, 1993. "Bayesian Treatment of the Independent Student- t Linear Model," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 8(S), pages S19-40, Suppl. De. [Downloadable!] (restricted)
  19. Jacquier, Eric & Polson, Nicholas G & Rossi, Peter E, 1994. "Bayesian Analysis of Stochastic Volatility Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(4), pages 371-89, October.
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  1. Markus Haas & Stefan Mittnik & Marc S. Paolella, 2006. "Multivariate Normal Mixture GARCH," CFS Working Paper Series 2006/09, Center for Financial Studies. [Downloadable!]
  2. 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. [Downloadable!]
  3. 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. [Downloadable!]
  4. Charles S. Bos & Ronald J. Mahieu & Herman K. van Dijk, 2001. "On the Variation of Hedging Decisions in Daily Currency Risk Management," Tinbergen Institute Discussion Papers 01-018/4, Tinbergen Institute. [Downloadable!]
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  5. L. Bauwens & C.S. Bos & H.K. Van Dijk & R.D. Van Oest, 2002. "Adaptive polar sampling, a class of flexibel and robust Monte Carlo integration methods," Econometric Institute Report 278, Erasmus University Rotterdam, Econometric Institute. [Downloadable!]
    Other versions:
  6. Luc, BAUWENS & Arie, PREMINGER & Jeroen, ROMBOUTS, 2006. "Regime switching GARCH models," Discussion Papers (ECON - Département des Sciences Economiques) 2006006, Université catholique de Louvain, Département des Sciences Economiques. [Downloadable!]
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