IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v78y2008i12p1480-1489.html
   My bibliography  Save this article

The autocorrelation structure of the Markov-switching asymmetric power GARCH process

Author

Listed:
  • Haas, Markus

Abstract

In a recent paper, Liu [Liu, J.-C., 2007. Stationarity for a Markov-switching Box-Cox transformed threshold GARCH process. Statistics and Probability Letters 77, 1428-1438] proposed a generalization of the Markov-switching GARCH model of Haas et al. [Haas, M., Mittnik, S., Paolella, M.S., 2004. A new approach to Markov-switching GARCH models. Journal of Financial Econometrics 2, 493-530] to allow for a nonlinear relation between past shocks and future volatility as well as for the leverage effect, which refers to the observation that stock market volatility reacts differently to positive and negative shocks. For the new model, Liu [Liu, J.-C., 2007. Stationarity for a Markov-switching Box-Cox transformed threshold GARCH process. Statistics and Probability Letters 77, 1428-1438] derived conditions for stationarity and the existence of moments. This article complements Liu's [Liu, J.-C., 2007. Stationarity for a Markov-switching Box-Cox transformed threshold GARCH process. Statistics and Probability Letters 77, 1428-1438] results in two directions. First, a simple method for calculating the moments and the autocorrelation structure of the power-transformed absolute process is devised, which is of vital interest in applied GARCH modeling. Second, in an application to stock returns, the relevance of the extended Markov-switching GARCH process proposed by Liu [Liu, J.-C., 2007. Stationarity for a Markov-switching Box-Cox transformed threshold GARCH process. Statistics and Probability Letters 77, 1428-1438], as compared to simpler versions, is illustrated.

Suggested Citation

  • Haas, Markus, 2008. "The autocorrelation structure of the Markov-switching asymmetric power GARCH process," Statistics & Probability Letters, Elsevier, vol. 78(12), pages 1480-1489, September.
    • Handle: RePEc:eee:stapro:v:78:y:2008:i:12:p:1480-1489
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-7152(07)00447-6
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Pierre Giot & Sébastien Laurent, 2003. "Value-at-risk for long and short trading positions," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 18(6), pages 641-663.
    2. Markus Haas, 2004. "A New Approach to Markov-Switching GARCH Models," Journal of Financial Econometrics, Oxford University Press, vol. 2(4), pages 493-530.
    3. Glosten, Lawrence R & Jagannathan, Ravi & Runkle, David E, 1993. "On the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks," Journal of Finance, American Finance Association, vol. 48(5), pages 1779-1801, December.
    4. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    5. Liu, Ji-Chun, 2006. "On the tail behaviors of Box-Cox transformed threshold GARCH(1,1) process," Statistics & Probability Letters, Elsevier, vol. 76(13), pages 1323-1330, July.
    6. Higgins, Matthew L & Bera, Anil K, 1992. "A Class of Nonlinear ARCH Models," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 33(1), pages 137-158, February.
    7. Hwang, S. Y. & Basawa, I. V., 2004. "Stationarity and moment structure for Box-Cox transformed threshold GARCH(1,1) processes," Statistics & Probability Letters, Elsevier, vol. 68(3), pages 209-220, July.
    8. Liu, Ji-Chun, 2006. "On The Tail Behaviors Of A Family Of Garch Processes," Econometric Theory, Cambridge University Press, vol. 22(5), pages 852-862, October.
    9. 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.
    10. 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.
    11. Ding, Zhuanxin & Granger, Clive W. J. & Engle, Robert F., 1993. "A long memory property of stock market returns and a new model," Journal of Empirical Finance, Elsevier, vol. 1(1), pages 83-106, June.
    12. Timmermann, Allan, 2000. "Moments of Markov switching models," Journal of Econometrics, Elsevier, vol. 96(1), pages 75-111, May.
    13. Karanasos, Menelaos & Kim, Jinki, 2006. "A re-examination of the asymmetric power ARCH model," Journal of Empirical Finance, Elsevier, vol. 13(1), pages 113-128, January.
    14. Bekaert, Geert & Wu, Guojun, 2000. "Asymmetric Volatility and Risk in Equity Markets," The Review of Financial Studies, Society for Financial Studies, vol. 13(1), pages 1-42.
    15. Brooks, Robert, 2007. "Power arch modelling of the volatility of emerging equity markets," Emerging Markets Review, Elsevier, vol. 8(2), pages 124-133, May.
    16. Francq, Christian & ZakoI¨an, Jean-Michel, 2005. "The L2-structures of standard and switching-regime GARCH models," Stochastic Processes and their Applications, Elsevier, vol. 115(9), pages 1557-1582, September.
    17. Liu, Ji-Chun, 2007. "Stationarity for a Markov-switching Box-Cox transformed threshold GARCH process," Statistics & Probability Letters, Elsevier, vol. 77(13), pages 1428-1438, July.
    18. Cai, Jun, 1994. "A Markov Model of Switching-Regime ARCH," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(3), pages 309-316, July.
    19. Brooks, Robert D. & Faff, Robert W. & McKenzie, Michael D. & Mitchell, Heather, 2000. "A multi-country study of power ARCH models and national stock market returns," Journal of International Money and Finance, Elsevier, vol. 19(3), pages 377-397, June.
    Full references (including those not matched with items on IDEAS)

    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. Carol Alexander & Emese Lazar, 2009. "Modelling Regime‐Specific Stock Price Volatility," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 71(6), pages 761-797, December.
    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. repec:awi:wpaper:0472 is not listed on IDEAS
    4. Charles, Amélie, 2010. "The day-of-the-week effects on the volatility: The role of the asymmetry," European Journal of Operational Research, Elsevier, vol. 202(1), pages 143-152, April.
    5. Conrad, Christian & Karanasos, Menelaos & Zeng, Ning, 2011. "Multivariate fractionally integrated APARCH modeling of stock market volatility: A multi-country study," Journal of Empirical Finance, Elsevier, vol. 18(1), pages 147-159, January.
    6. Degiannakis, Stavros & Xekalaki, Evdokia, 2004. "Autoregressive Conditional Heteroskedasticity (ARCH) Models: A Review," MPRA Paper 80487, University Library of Munich, Germany.
    7. Gerrit Reher & Bernd Wilfling, 2016. "A nesting framework for Markov-switching GARCH modelling with an application to the German stock market," Quantitative Finance, Taylor & Francis Journals, vol. 16(3), pages 411-426, March.
    8. Assaf, Ata, 2015. "Value-at-Risk analysis in the MENA equity markets: Fat tails and conditional asymmetries in return distributions," Journal of Multinational Financial Management, Elsevier, vol. 29(C), pages 30-45.
    9. Michael McKenzie & Heather Mitchell & Robert Brooks & Robert Faff, 2001. "Power ARCH modelling of commodity futures data on the London Metal Exchange," The European Journal of Finance, Taylor & Francis Journals, vol. 7(1), pages 22-38.
    10. Sajjad Rasoul & Coakley Jerry & Nankervis John C, 2008. "Markov-Switching GARCH Modelling of Value-at-Risk," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 12(3), pages 1-31, September.
    11. Ataurima Arellano, Miguel & Rodríguez, Gabriel, 2020. "Empirical modeling of high-income and emerging stock and Forex market return volatility using Markov-switching GARCH models," The North American Journal of Economics and Finance, Elsevier, vol. 52(C).
    12. Tim Bollerslev, 2008. "Glossary to ARCH (GARCH)," CREATES Research Papers 2008-49, Department of Economics and Business Economics, Aarhus University.
    13. Dominique Guegan & Bertrand K. Hassani, 2019. "Risk Measurement," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-02119256, HAL.
    14. Brooks, Robert D. & Faff, Robert W. & McKenzie, Michael D. & Mitchell, Heather, 2000. "A multi-country study of power ARCH models and national stock market returns," Journal of International Money and Finance, Elsevier, vol. 19(3), pages 377-397, June.
    15. Xekalaki, Evdokia & Degiannakis, Stavros, 2005. "Evaluating volatility forecasts in option pricing in the context of a simulated options market," Computational Statistics & Data Analysis, Elsevier, vol. 49(2), pages 611-629, April.
    16. Thomas Chuffart, 2015. "Selection Criteria in Regime Switching Conditional Volatility Models," Econometrics, MDPI, vol. 3(2), pages 1-28, May.
    17. Franses,Philip Hans & Dijk,Dick van, 2000. "Non-Linear Time Series Models in Empirical Finance," Cambridge Books, Cambridge University Press, number 9780521779654, September.
    18. Haas, Markus & Mittnik, Stefan, 2008. "Multivariate regimeswitching GARCH with an application to international stock markets," CFS Working Paper Series 2008/08, Center for Financial Studies (CFS).
    19. BAUWENS, Luc & HAFNER, Christian & LAURENT, Sébastien, 2011. "Volatility models," LIDAM Discussion Papers CORE 2011058, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
      • Bauwens, L. & Hafner, C. & Laurent, S., 2012. "Volatility Models," LIDAM Reprints ISBA 2012028, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
      • Bauwens, L. & Hafner C. & Laurent, S., 2011. "Volatility Models," LIDAM Discussion Papers ISBA 2011044, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    20. Turgut Kısınbay, 2010. "Predictive ability of asymmetric volatility models at medium-term horizons," Applied Economics, Taylor & Francis Journals, vol. 42(30), pages 3813-3829.
    21. Petropoulos, Fotios & Apiletti, Daniele & Assimakopoulos, Vassilios & Babai, Mohamed Zied & Barrow, Devon K. & Ben Taieb, Souhaib & Bergmeir, Christoph & Bessa, Ricardo J. & Bijak, Jakub & Boylan, Joh, 2022. "Forecasting: theory and practice," International Journal of Forecasting, Elsevier, vol. 38(3), pages 705-871.
      • Fotios Petropoulos & Daniele Apiletti & Vassilios Assimakopoulos & Mohamed Zied Babai & Devon K. Barrow & Souhaib Ben Taieb & Christoph Bergmeir & Ricardo J. Bessa & Jakub Bijak & John E. Boylan & Jet, 2020. "Forecasting: theory and practice," Papers 2012.03854, arXiv.org, revised Jan 2022.

    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:eee:stapro:v:78:y:2008:i:12:p:1480-1489. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    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.