Advanced Search
MyIDEAS: Login

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

Contents:

Author Info

  • 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.

Download Info

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
File URL: http://alfresco.uclouvain.be/alfresco/download/attach/workspace/SpacesStore/a23dd526-0a61-4421-a6a9-4ac2da270ffb/coredp_1999_57.pdf
Download Restriction: no

Bibliographic Info

Paper provided by Université catholique de Louvain, Center for Operations Research and Econometrics (CORE) in its series CORE Discussion Papers with number 1999057.

as in new window
Length:
Date of creation: 01 Oct 1999
Date of revision:
Handle: RePEc:cor:louvco:1999057

Contact details of provider:
Postal: Voie du Roman Pays 34, 1348 Louvain-la-Neuve (Belgium)
Phone: 32(10)474321
Fax: +32 10474304
Email:
Web page: http://www.uclouvain.be/core
More information through EDIRC

Related research

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

Other versions of this item:

Find related papers by JEL classification:

References

References listed on IDEAS
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.:
as in new window
  1. repec:dgr:uvatin:2099024 is not listed on IDEAS
  2. 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.
  3. 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.
  4. 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.
  5. Roberts, G. O. & Smith, A. F. M., 1994. "Simple conditions for the convergence of the Gibbs sampler and Metropolis-Hastings algorithms," Stochastic Processes and their Applications, Elsevier, vol. 49(2), pages 207-216, February.
  6. repec:dgr:uvatin:2098025 is not listed on IDEAS
  7. Jacquier, Eric & Polson, Nicholas G & Rossi, Peter E, 1994. "Bayesian Analysis of Stochastic Volatility Models: Comments: Reply," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(4), pages 413-17, October.
  8. Paap, Richard & van Dijk, Herman K, 2003. "Bayes Estimates of Markov Trends in Possibly Cointegrated Series: An Application to U.S. Consumption and Income," Journal of Business & Economic Statistics, American Statistical Association, vol. 21(4), pages 547-63, October.
  9. Frank Kleibergen & Herman K. van Dijk, 1998. "Bayesian Simultaneous Equations Analysis using Reduced Rank Structures," Tinbergen Institute Discussion Papers 98-025/4, Tinbergen Institute.
  10. Koop, G. & van Dijk, H.K., 1999. "Testing for integration using evolving trend and seasonal models: A Bayesian approach," Econometric Institute Research Papers EI 9934/A, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
  11. 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.
  12. Geweke, John, 1989. "Exact predictive densities for linear models with arch disturbances," Journal of Econometrics, Elsevier, vol. 40(1), pages 63-86, January.
  13. Sangjoon Kim, Neil Shephard & Siddhartha Chib, . "Stochastic volatility: likelihood inference and comparison with ARCH models," Economics Papers W26, revised version of W, Economics Group, Nuffield College, University of Oxford.
  14. repec:cup:etheor:v:12:y:1996:i:3:p:409-31 is not listed on IDEAS
  15. 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.
  16. Kleibergen, F.R. & van Dijk, H.K., 1997. "Bayesian Simultaneous Equations Analysis using Reduced Rank Structures," Econometric Institute Research Papers EI 9714/A, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
  17. 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.
  18. John Geweke, 1991. "Evaluating the accuracy of sampling-based approaches to the calculation of posterior moments," Staff Report 148, Federal Reserve Bank of Minneapolis.
  19. Nelson, Daniel B., 1990. "Stationarity and Persistence in the GARCH(1,1) Model," Econometric Theory, Cambridge University Press, vol. 6(03), pages 318-334, September.
  20. John Geweke, 1998. "Using simulation methods for Bayesian econometric models: inference, development, and communication," Staff Report 249, Federal Reserve Bank of Minneapolis.
  21. repec:cup:etheor:v:10:y:1994:i:3-4:p:514-51 is not listed on IDEAS
  22. 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.
  23. 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.
  24. 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.
  25. 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.
Full references (including those not matched with items on IDEAS)

Citations

Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
as in new window

Cited by:
  1. 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.
  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. 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.
  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. 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.
  6. Mohamed Saidane & Christian Lavergne, 2009. "Optimal Prediction with Conditionally Heteroskedastic Factor Analysed Hidden Markov Models," Computational Economics, Society for Computational Economics, vol. 34(4), pages 323-364, November.

Lists

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

Statistics

Access and download statistics

Corrections

When requesting a correction, please mention this item's handle: RePEc:cor:louvco:1999057. See general information about how to correct material in RePEc.

For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Alain GILLIS).

If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

If references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.

If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.

Please note that corrections may take a couple of weeks to filter through the various RePEc services.