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Small Sample Properties of Copula-GARCH Modelling: A Monte Carlo Study

Author

Listed:
  • Carluccio Bianchi

    (Department of Economics and Quantitative Methods, University of Pavia)

  • Dean Fantazzini

    (Moscow School of Economics)

  • Maria Elena De Giuli

    (Department of Economics and Quantitative Methods, University of Pavia)

  • Mario Maggi

    (Department of Economics and Quantitative Methods, University of Pavia)

Abstract

Copula-GARCH models have been recently proposed in the financial literature as a statistical tool to build flexible multivariate distributions. Our extensive simulation studies investigate the small sample properties of these models and examine how misspecification in the marginals may affect the estimation of the dependence function represented by the copula. We show that the use of normal marginals when the true Data Generating Process is leptokurtic or asymmetric, produces negatively biased estimates of the normal copula correlations. A striking result is that these biases reach their highest value when correlations are strongly negative, and viceversa. This result remains unchanged with both positively skewed and negatively skewed data, while no biases are found if the variables are uncorrelated. Besides, the effect of marginals asymmetry on correlations is smaller than that of leptokurtosis. We finally analyse the performance of these models in terms of numerical convergence and positive definiteness of the estimated copula correlation matrix.

Suggested Citation

  • Carluccio Bianchi & Dean Fantazzini & Maria Elena De Giuli & Mario Maggi, 2009. "Small Sample Properties of Copula-GARCH Modelling: A Monte Carlo Study," Quaderni di Dipartimento 093, University of Pavia, Department of Economics and Quantitative Methods.
    • Handle: RePEc:pav:wpaper:093
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    References listed on IDEAS

    as
    1. Whitney K. Newey & Douglas G. Steigerwald, 1997. "Asymptotic Bias for Quasi-Maximum-Likelihood Estimators in Conditional Heteroskedasticity Models," Econometrica, Econometric Society, vol. 65(3), pages 587-600, May.
    2. Chen, Xiaohong & Fan, Yanqin & Patton, Andrew J., 2004. "Simple tests for models of dependence between multiple financial time series, with applications to U.S. equity returns and exchange rates," LSE Research Online Documents on Economics 24681, London School of Economics and Political Science, LSE Library.
    3. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    4. Hansen, Bruce E, 1994. "Autoregressive Conditional Density Estimation," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 35(3), pages 705-730, August.
    5. Fantazzini, Dean, 2010. "Three-stage semi-parametric estimation of T-copulas: Asymptotics, finite-sample properties and computational aspects," Computational Statistics & Data Analysis, Elsevier, vol. 54(11), pages 2562-2579, November.
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    Cited by:

    1. Dean Fantazzini, 2022. "Crypto-Coins and Credit Risk: Modelling and Forecasting Their Probability of Death," JRFM, MDPI, vol. 15(7), pages 1-34, July.
    2. Dean Fantazzini, 2024. "Adaptive Conformal Inference for Computing Market Risk Measures: An Analysis with Four Thousand Crypto-Assets," JRFM, MDPI, vol. 17(6), pages 1-44, June.
    3. Fantazzini, Dean & Shangina, Tamara, 2019. "The importance of being informed: forecasting market risk measures for the Russian RTS index future using online data and implied volatility over two decades," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 55, pages 5-31.

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    More about this item

    Keywords

    Copulas; Copula-GARCH models; Maximum Likelihood; Simulation; Small Sample Properties.;
    All these keywords.

    JEL classification:

    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • 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
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques

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