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Positivity Constraints on the Conditional Variances in the Family of Conditional Correlation GARCH Models

Author

Listed:
  • Nakatani, Tomoaki

    (Dept. of Economic Statistics, Stockholm School of Economics)

  • Teräsvirta, Timo

    (CREATES, School of Economics and Management, University of Aarhus)

Abstract

In this article, we derive a set of necessary and sufficient conditions for positivity of the vector conditional variance equation in multivariate GARCH models with explicit modelling of conditional correlation. These models include the constant conditional correlation GARCH model of Bollerslev (1990) and its extensions. Under the new conditions, it is possible to introduce negative volatility spillovers in the model. An empirical example illustrates usefulness of having such conditions in practice.

Suggested Citation

  • Nakatani, Tomoaki & Teräsvirta, Timo, 2007. "Positivity Constraints on the Conditional Variances in the Family of Conditional Correlation GARCH Models," SSE/EFI Working Paper Series in Economics and Finance 675, Stockholm School of Economics, revised 14 Feb 2008.
    • Handle: RePEc:hhs:hastef:0675
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    References listed on IDEAS

    as
    1. Engle, Robert F. & Kroner, Kenneth F., 1995. "Multivariate Simultaneous Generalized ARCH," Econometric Theory, Cambridge University Press, vol. 11(1), pages 122-150, February.
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    10. Nelson, Daniel B & Cao, Charles Q, 1992. "Inequality Constraints in the Univariate GARCH Model," Journal of Business & Economic Statistics, American Statistical Association, vol. 10(2), pages 229-235, April.
    11. Annastiina Silvennoinen & Timo Teräsvirta, 2005. "Multivariate Autoregressive Conditional Heteroskedasticity with Smooth Transitions in Conditional Correlations," Research Paper Series 168, Quantitative Finance Research Centre, University of Technology, Sydney.
    12. 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.
    13. 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.
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    Cited by:

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    3. Ngene, Geoffrey & Post, Jordin A. & Mungai, Ann N., 2018. "Volatility and shock interactions and risk management implications: Evidence from the U.S. and frontier markets," Emerging Markets Review, Elsevier, vol. 37(C), pages 181-198.
    4. Tomasz Woźniak, 2018. "Granger-causal analysis of GARCH models: A Bayesian approach," Econometric Reviews, Taylor & Francis Journals, vol. 37(4), pages 325-346, April.
    5. Karanasos, Menelaos & Xu, Yongdeng & Yfanti, Stavroula, 2017. "Constrained QML Estimation for Multivariate Asymmetric MEM with Spillovers: The Practicality of Matrix Inequalities," Cardiff Economics Working Papers E2017/14, Cardiff University, Cardiff Business School, Economics Section.
    6. Chaudhuri, Kausik & Sen, Rituparna & Tan, Zheng, 2018. "Testing extreme dependence in financial time series," Economic Modelling, Elsevier, vol. 73(C), pages 378-394.
    7. Pedersen, Rasmus Søndergaard, 2017. "Inference and testing on the boundary in extended constant conditional correlation GARCH models," Journal of Econometrics, Elsevier, vol. 196(1), pages 23-36.
    8. Palandri, Alessandro, 2015. "Do negative and positive equity returns share the same volatility dynamics?," Journal of Banking & Finance, Elsevier, vol. 58(C), pages 486-505.
    9. Conrad, Christian & Weber, Enzo, 2013. "Measuring Persistence in Volatility Spillovers," VfS Annual Conference 2013 (Duesseldorf): Competition Policy and Regulation in a Global Economic Order 79850, Verein für Socialpolitik / German Economic Association.
    10. Ngene, Geoffrey M. & Lee Kim, Yea & Wang, Jinghua, 2019. "Who poisons the pool? Time-varying asymmetric and nonlinear causal inference between low-risk and high-risk bonds markets," Economic Modelling, Elsevier, vol. 81(C), pages 136-147.
    11. Carnero M. Angeles & Eratalay M. Hakan, 2014. "Estimating VAR-MGARCH models in multiple steps," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 18(3), pages 339-365, May.
    12. 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.
    13. Tomasz Wozniak, 2012. "Granger-causal analysis of VARMA-GARCH models," Economics Working Papers ECO2012/19, European University Institute.
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    15. Rayadurgam, Vikram Chandramouli & Mangalagiri, Jayasree, 2023. "Does inclusion of GARCH variance in deep learning models improve financial contagion prediction?," Finance Research Letters, Elsevier, vol. 54(C).
    16. López Cabrera, Brenda & Schulz, Franziska, 2016. "Volatility linkages between energy and agricultural commodity prices," Energy Economics, Elsevier, vol. 54(C), pages 190-203.
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    18. Haas, Markus & Liu, Ji-Chun, 2015. "Theory for a Multivariate Markov--switching GARCH Model with an Application to Stock Markets," VfS Annual Conference 2015 (Muenster): Economic Development - Theory and Policy 112855, Verein für Socialpolitik / German Economic Association.

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    More about this item

    Keywords

    Multivariate GARCH; positivity constraints; conditional correlation;
    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
    • G19 - Financial Economics - - General Financial Markets - - - Other

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