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Positivity constraints on the conditional variances in the family of conditional correlation GARCH models

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  • Nakatani, Tomoaki
  • Teräsvirta, Timo

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. Review of Economics and Statistics 72, 498-505] 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.

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  • Nakatani, Tomoaki & Teräsvirta, Timo, 2008. "Positivity constraints on the conditional variances in the family of conditional correlation GARCH models," Finance Research Letters, Elsevier, vol. 5(2), pages 88-95, June.
  • Handle: RePEc:eee:finlet:v:5:y:2008:i:2:p:88-95
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    Cited by:

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    2. Karanasos, Menelaos & Xu, Yongdeng, 2017. "Matrix Inequality Constraints for Vector (Asymmetric Power) GARCH/HEAVY Models and MEM with spillovers: some New (Mixture) Formulations," Cardiff Economics Working Papers E2017/14, Cardiff University, Cardiff Business School, Economics Section.
    3. Chaudhuri, Kausik & Sen, Rituparna & Tan, Zheng, 2018. "Testing extreme dependence in financial time series," Economic Modelling, Elsevier, vol. 73(C), pages 378-394.
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    5. 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 1-27, May.
    6. 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.
    7. Tomasz Wozniak, 2012. "Granger-causal analysis of VARMA-GARCH models," Economics Working Papers ECO2012/19, European University Institute.
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    9. Christian Conrad & Menelaos Karanasos, 2008. "Modeling Volatility Spillovers between the Variabilities of US Inflation and Output: the UECCC GARCH Model," Working Papers 0475, University of Heidelberg, Department of Economics, revised Sep 2008.
    10. Conrad, Christian & Weber, Enzo, 2013. "Measuring Persistence in Volatility Spillovers," Working Papers 0543, University of Heidelberg, Department of Economics.
    11. 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.
    12. Haas, Markus, 2010. "Covariance forecasts and long-run correlations in a Markov-switching model for dynamic correlations," Finance Research Letters, Elsevier, vol. 7(2), pages 86-97, June.
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    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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