IDEAS home Printed from https://ideas.repec.org/a/jof/jforec/v28y2009i3p247-265.html
   My bibliography  Save this article

On a dynamic mixture GARCH model

Author

Listed:
  • Xixin Cheng

    (Department of Statistics and Actuarial Science, University of Hong Kong)

  • Philip L. H. Yu

    (Department of Statistics and Actuarial Science, University of Hong Kong)

  • W. K. Li

    (Department of Statistics and Actuarial Science, University of Hong Kong)

Abstract

This paper proposes a new mixture GARCH model with a dynamic mixture proportion. The mixture Gaussian distribution of the error can vary from time to time. The Bayesian Information Criterion and the EM algorithm are used to estimate the number of parameters as well as the model parameters and their standard errors. The new model is applied to the S&P500 Index and Hang Seng Index and compared with GARCH models with Gaussian error and Student's t error. The result shows that the IGARCH effect in these index returns could be the result of the mixture of one stationary volatility component with another non-stationary volatility component. The VaR based on the new model performs better than traditional GARCH-based VaRs, especially in unstable stock markets. Copyright © 2008 John Wiley & Sons, Ltd.

Suggested Citation

  • Xixin Cheng & Philip L. H. Yu & W. K. Li, 2009. "On a dynamic mixture GARCH model," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 28(3), pages 247-265.
    • Handle: RePEc:jof:jforec:v:28:y:2009:i:3:p:247-265
    DOI: 10.1002/for.1093
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1002/for.1093
    File Function: Link to full text; subscription required
    Download Restriction: no
    File URL: https://libkey.io/10.1002/for.1093?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Markus Haas, 2004. "A New Approach to Markov-Switching GARCH Models," Journal of Financial Econometrics, Oxford University Press, vol. 2(4), pages 493-530.
    2. repec:bla:jfinan:v:44:y:1989:i:5:p:1115-53 is not listed on IDEAS
    3. Li, C W & Li, W K, 1996. "On a Double-Threshold Autoregressive Heteroscedastic Time Series Model," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 11(3), pages 253-274, May-June.
    4. Ruud, Paul A., 1991. "Extensions of estimation methods using the EM algorithm," Journal of Econometrics, Elsevier, vol. 49(3), pages 305-341, September.
    5. Berka, Martin, 2005. "General Equilibrium Model of Arbitrage Trade and Real Exchange Rate Persistence," MPRA Paper 234, University Library of Munich, Germany.
    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. Thomas Mikosch & Catalin Starica, 2004. "Non-stationarities in financial time series, the long range dependence and the IGARCH effects," Econometrics 0412005, University Library of Munich, Germany.
    8. Dumas, Bernard, 1992. "Dynamic Equilibrium and the Real Exchange Rate in a Spatially Separated World," The Review of Financial Studies, Society for Financial Studies, vol. 5(2), pages 153-180.
    9. Hamilton, James D. & Susmel, Raul, 1994. "Autoregressive conditional heteroskedasticity and changes in regime," Journal of Econometrics, Elsevier, vol. 64(1-2), pages 307-333.
    10. Michael, Panos & Nobay, A Robert & Peel, David A, 1997. "Transactions Costs and Nonlinear Adjustment in Real Exchange Rates: An Empirical Investigation," Journal of Political Economy, University of Chicago Press, vol. 105(4), pages 862-879, August.
    11. Sercu, Piet & Uppal, Raman & Van Hulle, Cynthia, 1995. "The Exchange Rate in the Presence of Transaction Costs: Implications for Tests of Purchasing Power Parity," Journal of Finance, American Finance Association, vol. 50(4), pages 1309-1319, September.
    12. Goldfeld, Stephen M. & Quandt, Richard E., 1973. "A Markov model for switching regressions," Journal of Econometrics, Elsevier, vol. 1(1), pages 3-15, March.
    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


    Cited by:

    1. Haas, Markus & Krause, Jochen & Paolella, Marc S. & Steude, Sven C., 2013. "Time-varying mixture GARCH models and asymmetric volatility," The North American Journal of Economics and Finance, Elsevier, vol. 26(C), pages 602-623.
    2. Haas Markus, 2010. "Skew-Normal Mixture and Markov-Switching GARCH Processes," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 14(4), pages 1-56, September.
    3. Klein, Tony & Walther, Thomas, 2016. "Oil price volatility forecast with mixture memory GARCH," Energy Economics, Elsevier, vol. 58(C), pages 46-58.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Frédérique Bec & Anders Rahbek & Neil Shephard, 2008. "The ACR Model: A Multivariate Dynamic Mixture Autoregression," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 70(5), pages 583-618, October.
    2. Billio, Monica & Casarin, Roberto & Osuntuyi, Anthony, 2016. "Efficient Gibbs sampling for Markov switching GARCH models," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 37-57.
    3. Frédérique Bec & Mélika Ben Salem & Marine Carrasco, 2010. "Detecting Mean Reversion in Real Exchange Rates from a Multiple Regime star Model," Annals of Economics and Statistics, GENES, issue 99-100, pages 395-427.
    4. Bec, Frédérique & Zeng, Songlin, 2013. "Are Southeast Asian real exchange rates mean reverting?," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 23(C), pages 265-282.
    5. Pavlidis, Efthymios G. & Paya, Ivan & Peel, David A., 2011. "Real exchange rates and time-varying trade costs," Journal of International Money and Finance, Elsevier, vol. 30(6), pages 1157-1179, October.
    6. Bauwens, Luc & Dufays, Arnaud & Rombouts, Jeroen V.K., 2014. "Marginal likelihood for Markov-switching and change-point GARCH models," Journal of Econometrics, Elsevier, vol. 178(P3), pages 508-522.
    7. Ivan Paya & David A. Peel, 2005. "A New Analysis Of The Determinants Of The Real Dollar-Sterling Exchange Rate: 1871-1994," Working Papers. Serie AD 2005-16, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
    8. Bauwens Luc & Storti Giuseppe, 2009. "A Component GARCH Model with Time Varying Weights," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 13(2), pages 1-33, May.
    9. Frédérique Bec & Mélika Ben Salem & Ronald MacDonald, 2006. "Real exchange rates and real interest rates : a nonlinear perspective," Recherches économiques de Louvain, De Boeck Université, vol. 72(2), pages 177-194.
    10. repec:lan:wpaper:2370 is not listed on IDEAS
    11. AUGUSTYNIAK, Maciej & BAUWENS, Luc & DUFAYS, Arnaud, 2016. "A New Approach to Volatility Modeling : The High-Dimensional Markov Model," LIDAM Discussion Papers CORE 2016042, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    12. Ivan Paya & David A. Peel, 2004. "Nonlinear Ppp Under The Gold Standard," Working Papers. Serie AD 2004-24, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
    13. repec:lan:wpaper:2451 is not listed on IDEAS
    14. Uctum, Remzi, 2007. "Économétrie des modèles à changement de régimes : un essai de synthèse," L'Actualité Economique, Société Canadienne de Science Economique, vol. 83(4), pages 447-482, décembre.
    15. Ivan Paya & David A. Peel, 2006. "Temporal aggregation of an ESTAR process: some implications for purchasing power parity adjustment," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(5), pages 655-668, July.
    16. repec:bla:econom:v:72:y:2005:i:3:p:413-430 is not listed on IDEAS
    17. repec:lan:wpaper:2593 is not listed on IDEAS
    18. Ivan Paya & David Peel, 2005. "The process followed by PPP data. On the properties of linearity tests," Applied Economics, Taylor & Francis Journals, vol. 37(21), pages 2515-2522.
    19. Mario Cerrato & Hyunsok Kim & Ronald MacDonald, 2008. "3-Regime symmetric STAR modeling and exchange rate reversion," Working Papers 2009_05, Business School - Economics, University of Glasgow, revised Feb 2009.
    20. Mario Cerrato & Hyunsok Kim & Ronald Macdonald, 2010. "Three‐Regime Asymmetric STAR Modeling and Exchange Rate Reversion," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 42(7), pages 1447-1467, October.
    21. Augustyniak, Maciej, 2014. "Maximum likelihood estimation of the Markov-switching GARCH model," Computational Statistics & Data Analysis, Elsevier, vol. 76(C), pages 61-75.
    22. Efthymios Pavlidis & Ivan Paya & David Peel, 2010. "Further empirical evidence on the consumption-real exchange rate anomaly," Working Papers 447022, Lancaster University Management School, Economics Department.
    23. Franses, Ph.H.B.F. & van Dijk, D.J.C., 2002. "A simple test for PPP among traded goods," Econometric Institute Research Papers EI 2002-02, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    24. Chang, Ming-Jen & Su, Che-Yi, 2014. "The dynamic relationship between exchange rates and macroeconomic fundamentals: Evidence from Pacific Rim countries," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 30(C), pages 220-246.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:jof:jforec:v:28:y:2009:i:3:p:247-265. See general information about how to correct material in RePEc.

    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 CitEc recognized a bibliographic reference but did not link an item in RePEc 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 RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Wiley-Blackwell Digital Licensing or Christopher F. Baum (email available below). General contact details of provider: http://www3.interscience.wiley.com/cgi-bin/jhome/2966 .

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

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.