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Copula-MGARCH with continuous covariance decomposition

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  • Herwartz, Helmut
  • Raters, Fabian H.C.

Abstract

The Copula-MGARCH (C-MGARCH) model by Lee and Long (2009) incorporates standardized copula distributed innovations in MGARCH models. We motivate an extension of the C-MGARCH model by means of a continuous decomposition of the innovations’ covariance matrix. An extended BEKK(1, 1) model with rotated standardized innovations is outlined for the bivariate case. The model parameters and the rotation angle are jointly estimated by means of Maximum Likelihood. We conduct an application to the log-differences of Euro/US-Dollar and Japanese Yen/US-Dollar daily exchange rates. In-sample information criteria and ex-ante portfolio Value-at-Risk coverage tests show that the enhanced flexibility of the rotated C-MGARCH is supported by the data.

Suggested Citation

  • Herwartz, Helmut & Raters, Fabian H.C., 2015. "Copula-MGARCH with continuous covariance decomposition," Economics Letters, Elsevier, vol. 133(C), pages 73-76.
    • Handle: RePEc:eee:ecolet:v:133:y:2015:i:c:p:73-76
    DOI: 10.1016/j.econlet.2015.05.023
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    References listed on IDEAS

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    1. Roy van der Weide, 2002. "GO-GARCH: a multivariate generalized orthogonal GARCH model," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 17(5), pages 549-564.
    2. Matthias R. Fengler & Helmut Herwartz & Christian Werner, 2012. "A Dynamic Copula Approach to Recovering the Index Implied Volatility Skew," Journal of Financial Econometrics, Oxford University Press, vol. 10(3), pages 457-493, June.
    3. Lee, Tae-Hwy & Long, Xiangdong, 2009. "Copula-based multivariate GARCH model with uncorrelated dependent errors," Journal of Econometrics, Elsevier, vol. 150(2), pages 207-218, June.
    4. Engle, Robert F. & Kroner, Kenneth F., 1995. "Multivariate Simultaneous Generalized ARCH," Econometric Theory, Cambridge University Press, vol. 11(1), pages 122-150, February.
    5. Weide, R. van der, 2002. "Generalized Orthogonal GARCH. A Multivariate GARCH model," CeNDEF Working Papers 02-02, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance.
    6. Christoffersen, Peter F, 1998. "Evaluating Interval Forecasts," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 841-862, November.
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    Cited by:

    1. Krämer, Walter & Wied, Dominik, 2015. "A simple and focused backtest of value at risk," Economics Letters, Elsevier, vol. 137(C), pages 29-31.

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    More about this item

    Keywords

    Copula; MGARCH; Covariance decomposition; Value-at-Risk;
    All these keywords.

    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
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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