IDEAS home Printed from https://ideas.repec.org/a/eee/econom/v159y2010i1p55-73.html
   My bibliography  Save this article

Efficient estimation of a multivariate multiplicative volatility model

Author

Listed:
  • Hafner, Christian M.
  • Linton, Oliver

Abstract

We propose a multivariate generalization of the multiplicative volatility model of Engle and Rangel (2008), which has a nonparametric long run component and a unit multivariate GARCH short run dynamic component. We suggest various kernel-based estimation procedures for the parametric and nonparametric components, and derive the asymptotic properties thereof. For the parametric part of the model, we obtain the semiparametric efficiency bound. Our method is applied to a bivariate stock index series. We find that the univariate model of Engle and Rangel (2008) appears to be violated in the data whereas our multivariate model is more consistent with the data.

Suggested Citation

  • Hafner, Christian M. & Linton, Oliver, 2010. "Efficient estimation of a multivariate multiplicative volatility model," Journal of Econometrics, Elsevier, vol. 159(1), pages 55-73, November.
    • Handle: RePEc:eee:econom:v:159:y:2010:i:1:p:55-73
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304-4076(10)00113-2
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

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

    Other versions of this item:

    References listed on IDEAS

    as
    1. Annastiina Silvennoinen & Timo Teräsvirta, 2009. "Modeling Multivariate Autoregressive Conditional Heteroskedasticity with the Double Smooth Transition Conditional Correlation GARCH Model," Journal of Financial Econometrics, Oxford University Press, vol. 7(4), pages 373-411, Fall.
    2. Catalin Starica, 2004. "Is GARCH(1,1) as good a model as the Nobel prize accolades would imply?," Econometrics 0411015, University Library of Munich, Germany.
    3. Weide, R. van der, 2002. "Generalized Orthogonal GARCH. A Multivariate GARCH model," CeNDEF Working Papers 02-02, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance.
    4. José Rangel & Robert Engle, 2012. "The Factor–Spline–GARCH Model for High and Low Frequency Correlations," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 30(1), pages 109-124.
    5. Luc Bauwens & Sébastien Laurent & Jeroen V. K. Rombouts, 2006. "Multivariate GARCH models: a survey," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(1), pages 79-109, January.
    6. Lorenzo Cappiello & Robert F. Engle & Kevin Sheppard, 2006. "Asymmetric Dynamics in the Correlations of Global Equity and Bond Returns," Journal of Financial Econometrics, Oxford University Press, vol. 4(4), pages 537-572.
    7. Andrew J. Patton, 2006. "Estimation of multivariate models for time series of possibly different lengths," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(2), pages 147-173, March.
    8. Kawakatsu, Hiroyuki, 2006. "Matrix exponential GARCH," Journal of Econometrics, Elsevier, vol. 134(1), pages 95-128, September.
    9. Pelletier, Denis, 2006. "Regime switching for dynamic correlations," Journal of Econometrics, Elsevier, vol. 131(1-2), pages 445-473.
    10. Engle, Robert F & Sheppard, Kevin K, 2001. "Theoretical and Empirical Properties of Dynamic Conditional Correlation Multivariate GARCH," University of California at San Diego, Economics Working Paper Series qt5s2218dp, Department of Economics, UC San Diego.
    11. Roy van der Weide, 2004. "Wake me up before you GO-GARCH," Computing in Economics and Finance 2004 316, Society for Computational Economics.
    12. Juan Rodríguez-Poo & Oliver Linton, 2001. "Nonparametric factor analysis of residual time series," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 10(1), pages 161-182, June.
    13. Engle, Robert, 2002. "Dynamic Conditional Correlation: A Simple Class of Multivariate Generalized Autoregressive Conditional Heteroskedasticity Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(3), pages 339-350, July.
    14. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    15. Andrew J. Patton, 2006. "Modelling Asymmetric Exchange Rate Dependence," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 47(2), pages 527-556, May.
    16. Pesaran, M. Hashem & Timmermann, Allan, 2004. "How costly is it to ignore breaks when forecasting the direction of a time series?," International Journal of Forecasting, Elsevier, vol. 20(3), pages 411-425.
    17. Bénédicte Vidaillet & V. d'Estaintot & P. Abécassis, 2005. "Introduction," Post-Print hal-00287137, HAL.
    18. I. D. Vrontos & P. Dellaportas & D. N. Politis, 2003. "A full-factor multivariate GARCH model," Econometrics Journal, Royal Economic Society, vol. 6(2), pages 312-334, December.
    19. Roy van der Weide, 2002. "GO-GARCH: a multivariate generalized orthogonal GARCH model," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 17(5), pages 549-564.
    20. Hafner, Christian M. & Preminger, Arie, 2009. "On asymptotic theory for multivariate GARCH models," Journal of Multivariate Analysis, Elsevier, vol. 100(9), pages 2044-2054, October.
    21. Lanne, Markku & Saikkonen, Pentti, 2007. "A Multivariate Generalized Orthogonal Factor GARCH Model," Journal of Business & Economic Statistics, American Statistical Association, vol. 25, pages 61-75, January.
    22. Jondeau, Eric & Rockinger, Michael, 2006. "The Copula-GARCH model of conditional dependencies: An international stock market application," Journal of International Money and Finance, Elsevier, vol. 25(5), pages 827-853, August.
    23. Comte, F. & Lieberman, O., 2003. "Asymptotic theory for multivariate GARCH processes," Journal of Multivariate Analysis, Elsevier, vol. 84(1), pages 61-84, January.
    24. Elias Masry, 1996. "Multivariate Local Polynomial Regression For Time Series:Uniform Strong Consistency And Rates," Journal of Time Series Analysis, Wiley Blackwell, vol. 17(6), pages 571-599, November.
    25. Tse, Y K & Tsui, Albert K C, 2002. "A Multivariate Generalized Autoregressive Conditional Heteroscedasticity Model with Time-Varying Correlations," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(3), pages 351-362, July.
    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. Takashi Isogai, 2015. "An Empirical Study of the Dynamic Correlation of Japanese Stock Returns," Bank of Japan Working Paper Series 15-E-7, Bank of Japan.
    2. Silvennoinen, Annastiina & Teräsvirta, Timo, 2007. "Multivariate GARCH models," SSE/EFI Working Paper Series in Economics and Finance 669, Stockholm School of Economics, revised 18 Jan 2008.
    3. de Almeida, Daniel & Hotta, Luiz K. & Ruiz, Esther, 2018. "MGARCH models: Trade-off between feasibility and flexibility," International Journal of Forecasting, Elsevier, vol. 34(1), pages 45-63.
    4. 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).
    5. Massimiliano Caporin & Michael McAleer, 2011. "Ranking Multivariate GARCH Models by Problem Dimension: An Empirical Evaluation," Working Papers in Economics 11/23, University of Canterbury, Department of Economics and Finance.
    6. Caporin, Massimiliano & McAleer, Michael, 2014. "Robust ranking of multivariate GARCH models by problem dimension," Computational Statistics & Data Analysis, Elsevier, vol. 76(C), pages 172-185.
    7. Andersen, Torben G. & Bollerslev, Tim & Christoffersen, Peter F. & Diebold, Francis X., 2013. "Financial Risk Measurement for Financial Risk Management," Handbook of the Economics of Finance, in: G.M. Constantinides & M. Harris & R. M. Stulz (ed.), Handbook of the Economics of Finance, volume 2, chapter 0, pages 1127-1220, Elsevier.
    8. Luc Bauwens & Sébastien Laurent & Jeroen V. K. Rombouts, 2006. "Multivariate GARCH models: a survey," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(1), pages 79-109, January.
    9. Bernardi, Mauro & Catania, Leopoldo, 2018. "Portfolio optimisation under flexible dynamic dependence modelling," Journal of Empirical Finance, Elsevier, vol. 48(C), pages 1-18.
    10. Ruili Sun & Tiefeng Ma & Shuangzhe Liu & Milind Sathye, 2019. "Improved Covariance Matrix Estimation for Portfolio Risk Measurement: A Review," JRFM, MDPI, vol. 12(1), pages 1-34, March.
    11. Mauro Bernardi & Leopoldo Catania, 2016. "Portfolio Optimisation Under Flexible Dynamic Dependence Modelling," Papers 1601.05199, arXiv.org.
    12. Tim Bollerslev, 2008. "Glossary to ARCH (GARCH)," CREATES Research Papers 2008-49, Department of Economics and Business Economics, Aarhus University.
    13. Audrone Virbickaite & M. Concepción Ausín & Pedro Galeano, 2015. "Bayesian Inference Methods For Univariate And Multivariate Garch Models: A Survey," Journal of Economic Surveys, Wiley Blackwell, vol. 29(1), pages 76-96, February.
    14. H. J. Turtle & Kainan Wang, 2014. "Modeling Conditional Covariances With Economic Information Instruments," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 32(2), pages 217-236, April.
    15. Santos, André A.P. & Moura, Guilherme V., 2014. "Dynamic factor multivariate GARCH model," Computational Statistics & Data Analysis, Elsevier, vol. 76(C), pages 606-617.
    16. Noureldin, Diaa & Shephard, Neil & Sheppard, Kevin, 2014. "Multivariate rotated ARCH models," Journal of Econometrics, Elsevier, vol. 179(1), pages 16-30.
    17. Kwangmin Jung & Donggyu Kim & Seunghyeon Yu, 2021. "Next Generation Models for Portfolio Risk Management: An Approach Using Financial Big Data," Papers 2102.12783, arXiv.org, revised Feb 2022.
    18. Andrea Silvestrini & David Veredas, 2008. "Temporal Aggregation Of Univariate And Multivariate Time Series Models: A Survey," Journal of Economic Surveys, Wiley Blackwell, vol. 22(3), pages 458-497, July.
    19. Otranto, Edoardo, 2010. "Identifying financial time series with similar dynamic conditional correlation," Computational Statistics & Data Analysis, Elsevier, vol. 54(1), pages 1-15, January.
    20. Paolella, Marc S. & Polak, Paweł & Walker, Patrick S., 2021. "A non-elliptical orthogonal GARCH model for portfolio selection under transaction costs," Journal of Banking & Finance, Elsevier, vol. 125(C).

    More about this item

    Keywords

    GARCH Kernel estimation Local stationarity Semiparametric;

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

    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:econom:v:159:y:2010:i:1:p:55-73. 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/locate/jeconom .

    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.