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MGARCH models: tradeoff between feasibility and flexibility

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  • Almeida, Daniel de
  • Hotta, Luiz

Abstract

The parameters of popular multivariate GARCH (MGARCH) models are restricted so that their estimation is feasible in large systems and covariance stationarity and positive definiteness of conditional covariance matrices are guaranteed. These restrictions limit the dynamics that the models can represent, assuming, for example, that volatilities evolve in an univariate fashion, not being related neither among them nor with the correlations. This paper updates previous surveyson parametric MGARCH models focusing on their limitations to represent the dynamics observed in real systems of financial returns. The conclusions are illustrated using simulated data and a five-dimensional system of exchange rate returns.

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  • Almeida, Daniel de & Hotta, Luiz, 2015. "MGARCH models: tradeoff between feasibility and flexibility," DES - Working Papers. Statistics and Econometrics. WS ws1516, Universidad Carlos III de Madrid. Departamento de Estadística.
  • Handle: RePEc:cte:wsrepe:ws1516
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    2. Carlos Trucíos & João H. G. Mazzeu & Marc Hallin & Luiz K. Hotta & Pedro L. Valls Pereira & Mauricio Zevallos, 2022. "Forecasting Conditional Covariance Matrices in High-Dimensional Time Series: A General Dynamic Factor Approach," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 41(1), pages 40-52, December.
    3. Ariana Paola Cortés Ángel & Mustafa Hakan Eratalay, 2022. "Deep diving into the S&P Europe 350 index network and its reaction to COVID-19," Journal of Computational Social Science, Springer, vol. 5(2), pages 1343-1408, November.
    4. Georgios Gioldasis & Antonio Musolesi & Michel Simioni, 2020. "Model uncertainty, nonlinearities and out-of-sample comparison: evidence from international technology diffusion," Working Papers hal-02790523, HAL.
    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. João F. Caldeira & Guilherme V. Moura & Francisco J. Nogales & André A. P. Santos, 2017. "Combining Multivariate Volatility Forecasts: An Economic-Based Approach," Journal of Financial Econometrics, Oxford University Press, vol. 15(2), pages 247-285.
    7. Ana Alzate-Ortega & Natalia Garzón & Jesús Molina-Muñoz, 2024. "Volatility Spillovers in Emerging Markets: Oil Shocks, Energy, Stocks, and Gold," Energies, MDPI, vol. 17(2), pages 1-19, January.
    8. Cristina Amado & Annastiina Silvennoinen & Timo Ter¨asvirta, 2018. "Models with Multiplicative Decomposition of Conditional Variances and Correlations," NIPE Working Papers 07/2018, NIPE - Universidade do Minho.
    9. Shimada, Junji & Tsukuda, Yoshihiko & Miyakoshi, Tatsuyoshi, 2021. "Who is the center of local currency Asian government bond markets?," Japan and the World Economy, Elsevier, vol. 59(C).
    10. Bollerslev, Tim & Patton, Andrew J. & Quaedvlieg, Rogier, 2020. "Multivariate leverage effects and realized semicovariance GARCH models," Journal of Econometrics, Elsevier, vol. 217(2), pages 411-430.
    11. Vogler, Jan & Golosnoy, Vasyl, 2023. "Unrestricted maximum likelihood estimation of multivariate realized volatility models," European Journal of Operational Research, Elsevier, vol. 304(3), pages 1063-1074.
    12. Georgios Gioldasis & Antonio Musolesi & Michel Simioni, 2021. "Interactive R&D Spillovers: an estimation strategy based on forecasting-driven model selection," Working Papers hal-03224910, HAL.
    13. Amendola, Alessandra & Braione, Manuela & Candila, Vincenzo & Storti, Giuseppe, 2020. "A Model Confidence Set approach to the combination of multivariate volatility forecasts," International Journal of Forecasting, Elsevier, vol. 36(3), pages 873-891.
    14. Jingwei Pan, 0000. "Evaluating Correlation Forecasts Under Asymmetric Loss," Proceedings of Economics and Finance Conferences 11413234, International Institute of Social and Economic Sciences.
    15. Gioldasis, Georgios & Musolesi, Antonio & Simioni, Michel, 2023. "Interactive R&D spillovers: An estimation strategy based on forecasting-driven model selection," International Journal of Forecasting, Elsevier, vol. 39(1), pages 144-169.
    16. Ángeles Cebrián-Hernández & Enrique Jiménez-Rodríguez, 2021. "Modeling of the Bitcoin Volatility through Key Financial Environment Variables: An Application of Conditional Correlation MGARCH Models," Mathematics, MDPI, vol. 9(3), pages 1-16, January.
    17. Marc Hallin & Carlos Trucíos, 2020. "Forecasting Value-at-Risk and Expected Shortfall in Large Portfolios: a General Dynamic Factor Approach," Working Papers ECARES 2020-50, ULB -- Universite Libre de Bruxelles.
    18. Georgios Gioldasis & Antonio Musolesi & Michel Simioni, 2021. "Interactive R&D Spillovers: An estimation strategy based on forecasting-driven model selection," SEEDS Working Papers 0621, SEEDS, Sustainability Environmental Economics and Dynamics Studies, revised Jun 2021.
    19. Moura, Guilherme V. & Santos, André A. P., 2019. "Comparing Forecasts of Extremely Large Conditional Covariance Matrices," DES - Working Papers. Statistics and Econometrics. WS 29291, Universidad Carlos III de Madrid. Departamento de Estadística.
    20. Văn, Lê & Bảo, Nguyễn Khắc Quốc, 2022. "The relationship between global stock and precious metals under Covid-19 and happiness perspectives," Resources Policy, Elsevier, vol. 77(C).
    21. Ariana Paola Cortés à ngel & Mustafa Hakan Eratalay, 2021. "Deedp Diving Into The S&P 350 Europe Index Network Ans Its Reaction To Covid-19," University of Tartu - Faculty of Economics and Business Administration Working Paper Series 134, Faculty of Economics and Business Administration, University of Tartu (Estonia).
    22. Fiszeder, Piotr & Fałdziński, Marcin, 2019. "Improving forecasts with the co-range dynamic conditional correlation model," Journal of Economic Dynamics and Control, Elsevier, vol. 108(C).
    23. Markus Vogl, 2022. "Quantitative modelling frontiers: a literature review on the evolution in financial and risk modelling after the financial crisis (2008–2019)," SN Business & Economics, Springer, vol. 2(12), pages 1-69, December.
    24. Georgios Gioldasis & Antonio Musolesi & Michel Simioni, 2020. "Model uncertainty, nonlinearities and out-of-sample comparison: evidence from international technology diffusion," SEEDS Working Papers 0120, SEEDS, Sustainability Environmental Economics and Dynamics Studies, revised Jan 2020.

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    BEKK;

    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
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics

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