Advanced Search
MyIDEAS: Login to save this paper or follow this series

Marginal Likelihood for Markov-Switching and Change-Point GARCH Models

Contents:

Author Info

  • Luc Bauwens
  • Arnaud Dufays
  • Jeroen V.K. Rombouts

Abstract

GARCH volatility models with fixed parameters are too restrictive for long time series due to breaks in the volatility process. Flexible alternatives are Markov-switching GARCH and change-point GARCH models. They require estimation by MCMC methods due to the path dependence problem. An unsolved issue is the computation of their marginal likelihood, which is essential for determining the number of regimes or change-points. We solve the problem by using particle MCMC, a technique proposed by Andrieu, Doucet and Holenstein (2010). We examine the performance of this new method on simulated data, and we illustrate its use on several return series.

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://www.cirpee.org/fileadmin/documents/Cahiers_2011/CIRPEE11-38.pdf
Download Restriction: no

Bibliographic Info

Paper provided by CIRPEE in its series Cahiers de recherche with number 1138.

as in new window
Length:
Date of creation: 2011
Date of revision:
Handle: RePEc:lvl:lacicr:1138

Contact details of provider:
Postal: CP 8888, succursale Centre-Ville, Montréal, QC H3C 3P8
Phone: (514) 987-8161
Web page: http://www.cirpee.org/
More information through EDIRC

Related research

Keywords: Bayesian inference; Simulation; GARCH; Markov-switching model; Change-point model; Marginal likelihood; Particle; MCMC;

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. Francq, Christian & ZakoI¨an, Jean-Michel, 2008. "Deriving the autocovariances of powers of Markov-switching GARCH models, with applications to statistical inference," Computational Statistics & Data Analysis, Elsevier, vol. 52(6), pages 3027-3046, February.
  2. Cristina Amado & Timo Teräsvirta, 2011. "Modelling Volatility by Variance Decomposition," CREATES Research Papers 2011-01, School of Economics and Management, University of Aarhus.
  3. Flury, Thomas & Shephard, Neil, 2011. "Bayesian Inference Based Only On Simulated Likelihood: Particle Filter Analysis Of Dynamic Economic Models," Econometric Theory, Cambridge University Press, vol. 27(05), pages 933-956, October.
  4. Jesus Fernandez-Villaverde & Juan F. Rubio-Ramirez, 2006. "Estimating Macroeconomic Models: A Likelihood Approach," NBER Technical Working Papers 0321, National Bureau of Economic Research, Inc.
  5. repec:ulb:ulbeco:2013/6500 is not listed on IDEAS
  6. Thomas Mikosch & Cătălin Stărică, 2004. "Nonstationarities in Financial Time Series, the Long-Range Dependence, and the IGARCH Effects," The Review of Economics and Statistics, MIT Press, vol. 86(1), pages 378-390, February.
  7. Gray, Stephen F., 1996. "Modeling the conditional distribution of interest rates as a regime-switching process," Journal of Financial Economics, Elsevier, vol. 42(1), pages 27-62, September.
  8. Thomas Mikosch & Catalin Starica, 2004. "Non-stationarities in financial time series, the long range dependence and the IGARCH effects," Econometrics 0412005, EconWPA.
  9. BAUWENS, Luc & PREMINGER, Arie & ROMBOUTS, Jeroen V.K., 2007. "Theory and inference for a Markov switching GARCH model," CORE Discussion Papers 2007055, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  10. Zhongfang He & John M. Maheu, 2009. "Real Time Detection of Structural Breaks in GARCH Models," Working Papers 09-31, Bank of Canada.
  11. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
  12. DUFAYS, Arnaud, 2012. "Infinite-state Markov-switching for dynamic volatility and correlation models," CORE Discussion Papers 2012043, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  13. Richard T. Baillie & Claudio Morana, 2007. "Modeling Long Memory and Structural Breaks in Conditional Variances: an Adaptive FIGARCH Approach," ICER Working Papers - Applied Mathematics Series 11-2007, ICER - International Centre for Economic Research.
  14. Chib S. & Jeliazkov I., 2001. "Marginal Likelihood From the Metropolis-Hastings Output," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 270-281, March.
  15. Godsill, Simon J. & Doucet, Arnaud & West, Mike, 2004. "Monte Carlo Smoothing for Nonlinear Time Series," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 156-168, January.
  16. Hamilton, James D. & Susmel, Raul, 1994. "Autoregressive conditional heteroskedasticity and changes in regime," Journal of Econometrics, Elsevier, vol. 64(1-2), pages 307-333.
  17. Christophe Andrieu & Arnaud Doucet & Roman Holenstein, 2010. "Particle Markov chain Monte Carlo methods," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 72(3), pages 269-342.
  18. 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.
  19. Sylvia Fruhwirth-Schnatter, 2004. "Estimating marginal likelihoods for mixture and Markov switching models using bridge sampling techniques," Econometrics Journal, Royal Economic Society, vol. 7(1), pages 143-167, 06.
  20. Griffin, J.E. & Steel, M.F.J., 2011. "Stick-breaking autoregressive processes," Journal of Econometrics, Elsevier, vol. 162(2), pages 383-396, June.
  21. Haas, Markus & Mittnik, Stefan & Paolella, Marc S., 2002. "Mixed normal conditional heteroskedasticity," CFS Working Paper Series 2002/10, Center for Financial Studies (CFS).
  22. Belleflamme,Paul & Peitz,Martin, 2010. "Industrial Organization," Cambridge Books, Cambridge University Press, number 9780521681599.
  23. Winfried Pohlmeier & Luc Bauwens & David Veredas, 2007. "High frequency financial econometrics. Recent developments," ULB Institutional Repository 2013/136223, ULB -- Universite Libre de Bruxelles.
  24. Ding, Zhuanxin & Granger, Clive W. J., 1996. "Modeling volatility persistence of speculative returns: A new approach," Journal of Econometrics, Elsevier, vol. 73(1), pages 185-215, July.
  25. Chib, Siddhartha, 1996. "Calculating posterior distributions and modal estimates in Markov mixture models," Journal of Econometrics, Elsevier, vol. 75(1), pages 79-97, November.
  26. Chib, Siddhartha, 1998. "Estimation and comparison of multiple change-point models," Journal of Econometrics, Elsevier, vol. 86(2), pages 221-241, June.
  27. Markus Haas, 2004. "A New Approach to Markov-Switching GARCH Models," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 2(4), pages 493-530.
  28. Geweke, John, 2007. "Interpretation and inference in mixture models: Simple MCMC works," Computational Statistics & Data Analysis, Elsevier, vol. 51(7), pages 3529-3550, April.
  29. Teh, Yee Whye & Jordan, Michael I. & Beal, Matthew J. & Blei, David M., 2006. "Hierarchical Dirichlet Processes," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1566-1581, December.
  30. Michael S. Johannes & Nicholas G. Polson & Jonathan R. Stroud, 2009. "Optimal Filtering of Jump Diffusions: Extracting Latent States from Asset Prices," Review of Financial Studies, Society for Financial Studies, vol. 22(7), pages 2559-2599, July.
  31. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
  32. Robert F. Engle & Jose Gonzalo Rangel, 2008. "The Spline-GARCH Model for Low-Frequency Volatility and Its Global Macroeconomic Causes," Review of Financial Studies, Society for Financial Studies, vol. 21(3), pages 1187-1222, May.
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. Rombouts, Jeroen V.K. & Stentoft, Lars, 2014. "Bayesian option pricing using mixed normal heteroskedasticity models," Computational Statistics & Data Analysis, Elsevier, vol. 76(C), pages 588-605.
  2. Augustyniak, Maciej, 2014. "Maximum likelihood estimation of the Markov-switching GARCH model," Computational Statistics & Data Analysis, Elsevier, vol. 76(C), pages 61-75.
  3. Menelaos Karanasos & Alexandros Paraskevopoulos & Faek Menla Ali & Michail Karoglou & Stavroula Yfanti, 2014. "Modelling Returns and Volatilities During Financial Crises: a Time Varying Coefficient Approach," Papers 1403.7179, arXiv.org.
  4. Jin, Xin & Maheu, John M, 2014. "Modeling Covariance Breakdowns in Multivariate GARCH," MPRA Paper 55243, University Library of Munich, Germany.
  5. repec:luc:wpaper:14-07 is not listed on IDEAS

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:lvl:lacicr:1138. 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: (Johanne Perron).

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.