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On The Relation Between The Vec And Bekk Multivariate Garch Models

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  • Stelzer, Robert

Abstract

The question of which multivariate generalized autoregressive conditionally heteroskedastic (GARCH) models in the vec form are representable in the BEKK form is addressed. Using results from linear algebra, it is established that all vec models not representable in the simplest BEKK form contain matrices as parameters that map the vectorized positive semidefinite matrices into a strict subset of themselves. Moreover, a general result from linear algebra is presented implying that in dimension two the models are equivalent, and in dimension three a simple analytically tractable example for a vec model having no BEKK representation is given.

Suggested Citation

  • Stelzer, Robert, 2008. "On The Relation Between The Vec And Bekk Multivariate Garch Models," Econometric Theory, Cambridge University Press, vol. 24(4), pages 1131-1136, August.
    • Handle: RePEc:cup:etheor:v:24:y:2008:i:04:p:1131-1136_08
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    1. Boussama, Farid & Fuchs, Florian & Stelzer, Robert, 2011. "Stationarity and geometric ergodicity of BEKK multivariate GARCH models," Stochastic Processes and their Applications, Elsevier, vol. 121(10), pages 2331-2360, October.
    2. Philipp Otto & Osman Dou{g}an & Suleyman Tac{s}p{i}nar & Wolfgang Schmid & Anil K. Bera, 2023. "Spatial and Spatiotemporal Volatility Models: A Review," Papers 2308.13061, arXiv.org.
    3. Yip, Iris W.H. & So, Mike K.P., 2009. "Simplified specifications of a multivariate generalized autoregressive conditional heteroscedasticity model," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 80(2), pages 327-340.
    4. Wen, Danyan & Wang, Yudong & Ma, Chaoqun & Zhang, Yaojie, 2020. "Information transmission between gold and financial assets: Mean, volatility, or risk spillovers?," Resources Policy, Elsevier, vol. 69(C).
    5. Villalba Padilla, Fátima Irina & Flores-Ortega, Miguel, 2014. "Análisis de la volatilidad del índice principal del mercado bursátil mexicano, del índice de riesgo país y de la mezcla mexicana de exportación mediante un modelo GARCH trivariado asimétrico || Volati," Revista de Métodos Cuantitativos para la Economía y la Empresa = Journal of Quantitative Methods for Economics and Business Administration, Universidad Pablo de Olavide, Department of Quantitative Methods for Economics and Business Administration, vol. 17(1), pages 3-22, June.
    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. Resende, Paulo Angelo Alves & Dorea, Chang Chung Yu, 2016. "Model identification using the Efficient Determination Criterion," Journal of Multivariate Analysis, Elsevier, vol. 150(C), pages 229-244.
    8. Fengler, Matthias R. & Herwartz, Helmut, 2015. "Measuring spot variance spillovers when (co)variances are time-varying – the case of multivariate GARCH models," Economics Working Paper Series 1517, University of St. Gallen, School of Economics and Political Science.
    9. Avarucci, Marco & Beutner, Eric & Zaffaroni, Paolo, 2013. "On Moment Conditions For Quasi-Maximum Likelihood Estimation Of Multivariate Arch Models," Econometric Theory, Cambridge University Press, vol. 29(3), pages 545-566, June.
    10. Yu, Lean & Zha, Rui & Stafylas, Dimitrios & He, Kaijian & Liu, Jia, 2020. "Dependences and volatility spillovers between the oil and stock markets: New evidence from the copula and VAR-BEKK-GARCH models," International Review of Financial Analysis, Elsevier, vol. 68(C).

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