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Ranking Multivariate GARCH Models by Problem Dimension

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  • Massimiliano Caporin

    (Department of Economics and Management "Marco Fanno", University of Padova)

  • Michael McAleer

    (Erasmus School of Economics, Erasmus University Rotterdam, Tinbergen Institute and Department of Economics and Finance, University of Canterbury)

Abstract

In the last 15 years, several Multivariate GARCH (MGARCH) models have appeared in the literature. The two most widely known and used are the Scalar BEKK model of Engle and Kroner (1995) and Ding and Engle (2001), and the DCC model of Engle (2002). Some recent research has begun to examine MGARCH specifications in terms of their out-of-sample forecasting performance. In this paper, we provide an empirical comparison of a set of MGARCH models, namely BEKK, DCC, Corrected DCC (cDCC) of Aeilli (2008), CCC of Bollerslev (1990), Exponentially Weighted Moving Average, and covariance shrinking of Ledoit and Wolf (2004), using the historical data of 89 US equities. Our methods follow some of the approach described in Patton and Sheppard (2009), and contribute to the literature in several directions. First, we consider a wide range of models, including the recent cDCC model and covariance shrinking. Second, we use a range of tests and approaches for direct and indirect model comparison, including the Weighted Likelihood Ratio test of Amisano and Giacomini (2007). Third, we examine how the model rankings are influenced by the cross-sectional dimension of the problem.

Suggested Citation

  • Massimiliano Caporin & Michael McAleer, 2010. "Ranking Multivariate GARCH Models by Problem Dimension," CARF F-Series CARF-F-219, Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo.
  • Handle: RePEc:cfi:fseres:cf219
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    Cited by:

    1. Sébastien Laurent & Jeroen V. K. Rombouts & Francesco Violante, 2012. "On the forecasting accuracy of multivariate GARCH models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 27(6), pages 934-955, September.
    2. Yaya, OlaOluwa & Ogbonna, Ahamuefula, 2018. "Modelling crude oil-petroleum products’ price nexus using dynamic conditional correlation GARCH models," MPRA Paper 91227, University Library of Munich, Germany.
    3. Massimiliano Caporin & Paolo Paruolo, 2015. "Proximity-Structured Multivariate Volatility Models," Econometric Reviews, Taylor & Francis Journals, vol. 34(5), pages 559-593, May.
    4. Zolfaghari, Mehdi, 2023. "How does US tariff policy affect the relationship among crude oil, the US dollar and metal markets?," Resources Policy, Elsevier, vol. 85(PB).
    5. Rombouts, Jeroen & Stentoft, Lars & Violante, Franceso, 2014. "The value of multivariate model sophistication: An application to pricing Dow Jones Industrial Average options," International Journal of Forecasting, Elsevier, vol. 30(1), pages 78-98.
    6. Adam E Clements & Mark Doolan & Stan Hurn & Ralf Becker, 2012. "Selecting forecasting models for portfolio allocation," NCER Working Paper Series 85, National Centre for Econometric Research.
    7. Fresoli, Diego E. & Ruiz, Esther, 2016. "The uncertainty of conditional returns, volatilities and correlations in DCC models," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 170-185.
    8. Benjamin Poignard & Jean-Davis Fermanian, 2014. "Dynamic Asset Correlations Based on Vines," Working Papers 2014-46, Center for Research in Economics and Statistics.
    9. Ralf Becker & Adam Clements & Robert O'Neill, 2018. "A Multivariate Kernel Approach to Forecasting the Variance Covariance of Stock Market Returns," Econometrics, MDPI, vol. 6(1), pages 1-27, February.
    10. Adam E Clements & Ayesha Scott & Annastiina Silvennoinen, 2012. "Forecasting multivariate volatility in larger dimensions: some practical issues," NCER Working Paper Series 80, National Centre for Econometric Research.
    11. Salisu, Afees A. & Oloko, Tirimisiyu F., 2015. "Modeling oil price–US stock nexus: A VARMA–BEKK–AGARCH approach," Energy Economics, Elsevier, vol. 50(C), pages 1-12.
    12. Caporin, M. & McAleer, M.J., 2010. "Model Selection and Testing of Conditional and Stochastic Volatility Models," Econometric Institute Research Papers EI 2010-57, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    13. Adam Clements & Ayesha Scott & Annastiina Silvennoinen, 2013. "On the Benefits of Equicorrelation for Portfolio Allocation," NCER Working Paper Series 99, National Centre for Econometric Research.
    14. Becker, R. & Clements, A.E. & Doolan, M.B. & Hurn, A.S., 2015. "Selecting volatility forecasting models for portfolio allocation purposes," International Journal of Forecasting, Elsevier, vol. 31(3), pages 849-861.
    15. Manner, Hans & Reznikova, Olga, 2010. "Forecasting international stock market correlations: does anything beat a CCC?," Discussion Papers in Econometrics and Statistics 7/10, University of Cologne, Institute of Econometrics and Statistics.

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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
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection

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