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Vine-copula GARCH model with dynamic conditional dependence

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  • So, Mike K.P.
  • Yeung, Cherry Y.T.

Abstract

Constructing multivariate conditional distributions for non-Gaussian return series has been a major research agenda recently. Copula GARCH models combine the use of GARCH models and a copula function to allow flexibility on the choice of marginal distributions and dependence structures. However, it is non-trivial to define multivariate copula densities that allow dynamic dependent structures in returns. The vine-copula method has been gaining attention recently in that a multi-dimensional density can be decomposed into a product of conditional bivariate copulas and marginal densities. The dependence structure is interpreted individually in each copula pair. Yet, most studies have only focused on time varying correlation. A vine-copula GARCH model with dynamic conditional dependence is proposed. A generic approach to specifying dynamic conditional dependence using any dependence measures is developed. The characterization also induces multivariate conditional dependence dynamically through vine decomposition. The main idea is to incorporate dynamic conditional dependence, such as Kendall’s tau and rank correlation, not to mention linear correlation, in each bivariate copula pair. The estimation is conducted through a sequential approach. Simulation experiments are performed and five Hong Kong blue chip stock data from January 2004 to December 2011 are studied. Using t and two Archimedean copulas, it is revealed that Kendall’s tau and linear correlation of the stock returns vary over time, indicating the presence of time varying properties in dependence.

Suggested Citation

  • So, Mike K.P. & Yeung, Cherry Y.T., 2014. "Vine-copula GARCH model with dynamic conditional dependence," Computational Statistics & Data Analysis, Elsevier, vol. 76(C), pages 655-671.
  • Handle: RePEc:eee:csdana:v:76:y:2014:i:c:p:655-671
    DOI: 10.1016/j.csda.2013.08.008
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    3. Giuseppe Arbia & Riccardo Bramante & Silvia Facchinetti, 2020. "Least Quartic Regression Criterion to Evaluate Systematic Risk in the Presence of Co-Skewness and Co-Kurtosis," Risks, MDPI, vol. 8(3), pages 1-14, September.
    4. Jiang, Cuixia & Li, Yuqian & Xu, Qifa & Liu, Yezheng, 2021. "Measuring risk spillovers from multiple developed stock markets to China: A vine-copula-GARCH-MIDAS model," International Review of Economics & Finance, Elsevier, vol. 75(C), pages 386-398.
    5. Dominique Guegan & Matteo Iacopini, 2018. "Nonparametric forecasting of multivariate probability density functions," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-01821815, HAL.
    6. Tófoli Paula V. & Ziegelmann Flávio A. & Candido Osvaldo & Valls Pereira Pedro L., 2019. "Dynamic D-Vine Copula Model with Applications to Value-at-Risk (VaR)," Journal of Time Series Econometrics, De Gruyter, vol. 11(2), pages 1-34, July.
    7. Quanrui Song & Jianxu Liu & Songsak Sriboonchitta, 2019. "Risk Measurement of Stock Markets in BRICS, G7, and G20: Vine Copulas versus Factor Copulas," Mathematics, MDPI, vol. 7(3), pages 1-16, March.
    8. Timothy M. Young & Ampalavanar Nanthakumar & Hari Nanthakumar, 2021. "On the Use of Copula for Quality Control Based on an AR(1) Model," Mathematics, MDPI, vol. 9(18), pages 1-13, September.
    9. 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.
    10. 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.
    11. Han, Yingwei & Li, Jie, 2022. "Should investors include green bonds in their portfolios? Evidence for the USA and Europe," International Review of Financial Analysis, Elsevier, vol. 80(C).
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    13. Han, Xuyuan & Liu, Zhenya & Wang, Shixuan, 2022. "An R-vine copula analysis of non-ferrous metal futures with application in Value-at-Risk forecasting," Journal of Commodity Markets, Elsevier, vol. 25(C).
    14. Zhang, Bangzheng & Wei, Yu & Yu, Jiang & Lai, Xiaodong & Peng, Zhenfeng, 2014. "Forecasting VaR and ES of stock index portfolio: A Vine copula method," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 416(C), pages 112-124.
    15. Amanda M. Y. Chu & Thomas W. C. Chan & Mike K. P. So & Wing-Keung Wong, 2021. "Dynamic Network Analysis of COVID-19 with a Latent Pandemic Space Model," IJERPH, MDPI, vol. 18(6), pages 1-22, March.
    16. Dominique Guegan & Matteo Iacopini, 2018. "Nonparametric forecasting of multivariate probability density functions," Post-Print halshs-01821815, HAL.
    17. Dominique Guégan & Matteo Iacopini, 2018. "Nonparameteric forecasting of multivariate probability density functions," Documents de travail du Centre d'Economie de la Sorbonne 18012, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    18. Kjersti Aas, 2016. "Pair-Copula Constructions for Financial Applications: A Review," Econometrics, MDPI, vol. 4(4), pages 1-15, October.
    19. Jianxu Liu & Mengjiao Wang & Songsak Sriboonchitta, 2019. "Examining the Interdependence between the Exchange Rates of China and ASEAN Countries: A Canonical Vine Copula Approach," Sustainability, MDPI, vol. 11(19), pages 1-20, October.
    20. Derumigny, Alexis & Fermanian, Jean-David, 2019. "A classification point-of-view about conditional Kendall’s tau," Computational Statistics & Data Analysis, Elsevier, vol. 135(C), pages 70-94.
    21. Zhou, Rui & Ji, Min, 2021. "Modelling mortality dependence: An application of dynamic vine copula," Insurance: Mathematics and Economics, Elsevier, vol. 99(C), pages 241-255.
    22. Rewat Khanthaporn, 2022. "Analysis of Nonlinear Comovement of Benchmark Thai Government Bond Yields," PIER Discussion Papers 183, Puey Ungphakorn Institute for Economic Research.
    23. Acar, Elif F. & Czado, Claudia & Lysy, Martin, 2019. "Flexible dynamic vine copula models for multivariate time series data," Econometrics and Statistics, Elsevier, vol. 12(C), pages 181-197.
    24. Do, A. & Powell, R. & Yong, J. & Singh, A., 2020. "Time-varying asymmetric volatility spillover between global markets and China’s A, B and H-shares using EGARCH and DCC-EGARCH models," The North American Journal of Economics and Finance, Elsevier, vol. 54(C).
    25. So, Mike K.P. & Chan, Thomas W.C. & Chu, Amanda M.Y., 2022. "Efficient estimation of high-dimensional dynamic covariance by risk factor mapping: Applications for financial risk management," Journal of Econometrics, Elsevier, vol. 227(1), pages 151-167.

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