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Thresholds, News Impact Surfaces and Dynamic Asymmetric Multivariate GARCH

Author

Listed:
  • Massimiliano Caporin

    (Department of Economic Sciences University of Padova)

  • Michael McAleer

    (Universidad Complutense de Madrid.Department of Quantitative Economics)

Abstract

DAMGARCH is a new model that extends the VARMA-GARCH model of Ling and McAleer (2003) by introducing multiple thresholds and time-dependent structure in the asymmetry of the conditional variances. Analytical expressions for the news impact surface implied by the new model are also presented. DAMGARCH models the shocks affecting the conditional variances on the basis of an underlying multivariate distribution. It is possible to model explicitly asset-specific shocks and common innovations by partitioning the multivariate density support. This paper presents the model structure, describes the implementation issues, and provides the conditions for the existence of a unique stationary solution, and for consistency and asymptotic normality of the quasi-maximum likelihood estimators. The paper also presents an empirical example to highlight the usefulness of the new model

Suggested Citation

  • Massimiliano Caporin & Michael McAleer, 2009. "Thresholds, News Impact Surfaces and Dynamic Asymmetric Multivariate GARCH," Documentos de Trabajo del ICAE 2009-11, Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales, Instituto Complutense de Análisis Económico.
    • Handle: RePEc:ucm:doicae:0911
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    File URL: https://eprints.ucm.es/id/eprint/8609/1/0911.pdf
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    References listed on IDEAS

    as
    1. McAleer, Michael & Chan, Felix & Marinova, Dora, 2007. "An econometric analysis of asymmetric volatility: Theory and application to patents," Journal of Econometrics, Elsevier, vol. 139(2), pages 259-284, August.
    2. Kroner, Kenneth F & Ng, Victor K, 1998. "Modeling Asymmetric Comovements of Asset Returns," The Review of Financial Studies, Society for Financial Studies, vol. 11(4), pages 817-844.
    3. Hafner, Christian M. & Herwartz, Helmut, 1999. "Time-varying market price of risk in the CAPM: Approaches, empirical evidence and implications," SFB 373 Discussion Papers 1999,22, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    4. Ling, Shiqing & McAleer, Michael, 2003. "Asymptotic Theory For A Vector Arma-Garch Model," Econometric Theory, Cambridge University Press, vol. 19(2), pages 280-310, April.
    5. Engle, Robert F. & Kroner, Kenneth F., 1995. "Multivariate Simultaneous Generalized ARCH," Econometric Theory, Cambridge University Press, vol. 11(1), pages 122-150, February.
    6. Michael McAleer & Suhejla Hoti & Felix Chan, 2009. "Structure and Asymptotic Theory for Multivariate Asymmetric Conditional Volatility," Econometric Reviews, Taylor & Francis Journals, vol. 28(5), pages 422-440.
    7. Peter de Goeij, 2004. "Modeling the Conditional Covariance Between Stock and Bond Returns: A Multivariate GARCH Approach," Journal of Financial Econometrics, Oxford University Press, vol. 2(4), pages 531-564.
    8. 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.
    9. Ling, Shiqing & McAleer, Michael, 2002. "NECESSARY AND SUFFICIENT MOMENT CONDITIONS FOR THE GARCH(r,s) AND ASYMMETRIC POWER GARCH(r,s) MODELS," Econometric Theory, Cambridge University Press, vol. 18(3), pages 722-729, June.
    10. Massimiliano Caporin & Michael McAleer, 2008. "Scalar BEKK and indirect DCC," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 27(6), pages 537-549.
    11. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    12. 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.
    13. Comte, F. & Lieberman, O., 2003. "Asymptotic theory for multivariate GARCH processes," Journal of Multivariate Analysis, Elsevier, vol. 84(1), pages 61-84, January.
    14. Massimiliano Caporin & Michael McAleer, 2009. "Do We Really Need Both BEKK and DCC? A Tale of Two Covariance Models," CARF F-Series CARF-F-156, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
    15. Rabemananjara, R & Zakoian, J M, 1993. "Threshold Arch Models and Asymmetries in Volatility," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 8(1), pages 31-49, Jan.-Marc.
    16. McAleer, Michael, 2005. "Automated Inference And Learning In Modeling Financial Volatility," Econometric Theory, Cambridge University Press, vol. 21(1), pages 232-261, February.
    17. 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.
    18. Jeantheau, Thierry, 1998. "Strong Consistency Of Estimators For Multivariate Arch Models," Econometric Theory, Cambridge University Press, vol. 14(1), pages 70-86, February.
    19. Shiqing Ling & W. K. Li, 1997. "Diagnostic checking of nonlinear multivariate time series with multivariate arch errors," Journal of Time Series Analysis, Wiley Blackwell, vol. 18(5), pages 447-464, September.
    20. Ling, Shiqing & McAleer, Michael, 2002. "Stationarity and the existence of moments of a family of GARCH processes," Journal of Econometrics, Elsevier, vol. 106(1), pages 109-117, January.
    21. Engle, Robert F & Ng, Victor K, 1993. "Measuring and Testing the Impact of News on Volatility," Journal of Finance, American Finance Association, vol. 48(5), pages 1749-1778, December.
    22. Bollerslev, Tim & Chou, Ray Y. & Kroner, Kenneth F., 1992. "ARCH modeling in finance : A review of the theory and empirical evidence," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 5-59.
    23. Bollerslev, Tim, 1990. "Modelling the Coherence in Short-run Nominal Exchange Rates: A Multivariate Generalized ARCH Model," The Review of Economics and Statistics, MIT Press, vol. 72(3), pages 498-505, August.
    24. repec:bla:jecsur:v:16:y:2002:i:3:p:245-69 is not listed on IDEAS
    25. Bjorn Hansson & Peter Hordahl, 1998. "Testing the conditional CAPM using multivariate GARCH-M," Applied Financial Economics, Taylor & Francis Journals, vol. 8(4), pages 377-388.
    26. W. K. Li & Shiqing Ling & Michael McAleer, 2002. "Recent Theoretical Results for Time Series Models with GARCH Errors," Journal of Economic Surveys, Wiley Blackwell, vol. 16(3), pages 245-269, July.
    27. McAleer, Michael & Chan, Felix & Hoti, Suhejla & Lieberman, Offer, 2008. "Generalized Autoregressive Conditional Correlation," Econometric Theory, Cambridge University Press, vol. 24(6), pages 1554-1583, December.
    28. de Goeij, P. C. & Marquering, W., 2004. "Modeling the conditional covariance between stock and bond returns : A multivariate GARCH approach," Other publications TiSEM 94fe5ada-715a-4339-b94c-f, Tilburg University, School of Economics and Management.
    29. 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.
    30. 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.
    31. Massimiliano Caporin & Michael McAleer, 2006. "Dynamic Asymmetric GARCH," Journal of Financial Econometrics, Oxford University Press, vol. 4(3), pages 385-412.
    32. 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.
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    Cited by:

    1. Asai, Manabu & McAleer, Michael, 2015. "Forecasting co-volatilities via factor models with asymmetry and long memory in realized covariance," Journal of Econometrics, Elsevier, vol. 189(2), pages 251-262.
    2. 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.
    3. Rombouts, Jeroen & Stentoft, Lars & Violante, Franceso, 2014. "The value of multivariate model sophistication: An application to pricing Dow Jones Industrial Average options," International Journal of Forecasting, Elsevier, vol. 30(1), pages 78-98.
    4. repec:cte:wsrepe:ws131110 is not listed on IDEAS
    5. Oscar Espinosa & Fabio Nieto, 2020. "A study on the leverage effect on financial series using a TAR model: a Bayesian approach," Papers 2002.05319, arXiv.org, revised Feb 2020.
    6. Alexander HARIN, 2014. "Partially Unforeseen Events. Corrections and Correcting Formulae for Forecasts," Expert Journal of Economics, Sprint Investify, vol. 2(2), pages 69-79.
    7. Asai, Manabu & McAleer, Michael, 2008. "A Portfolio Index GARCH model," International Journal of Forecasting, Elsevier, vol. 24(3), pages 449-461.
    8. Harin, Alexander, 2014. "General correcting formulae for forecasts," MPRA Paper 55283, University Library of Munich, Germany.

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    More about this item

    Keywords

    multivariate asymmetry; conditional variance; stationarity conditions; asymptotic theory; multivariate news impact curve.;
    All these keywords.

    JEL classification:

    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection

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