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Analysis of multidimensional probability distributions with copula functions

Author

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  • Fantazzini, Dean

    () (Moscow School of Economics, Moscow State University)

Abstract

Problems which are related to copula functions, their properties, selection methods for specific baseline data, evaluation, and possible applications are extremely sparingly discussed in the world literature, and are almost not discussed at all in the Russian literature. At the same time, we already had impressive examples of their applications in situations when the construction, statistical estimation and analysis of multidimensional probability distributions turn out to be an essential tool of applied research, and the use of the multivariate normal (Gaussian) distributions for these purposes does not reflect the specific features of the available data. There are grounds to argue that models which are based on copula functions will be in particular demand for applied econometric studies regarding problems of assessment, analysis and management of financial and insurance risks, as well as the returns of various financial instruments. The material proposed in this issue of the journal is, in fact, a fragment of the forthcoming textbook «Methods of econometrics. Advanced level» by S. A. Aivazian, D. Fantazzini

Suggested Citation

  • Fantazzini, Dean, 2011. "Analysis of multidimensional probability distributions with copula functions," Applied Econometrics, Publishing House "SINERGIA PRESS", vol. 22(2), pages 98-134.
  • Handle: RePEc:ris:apltrx:0077
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    References listed on IDEAS

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    1. Aas, Kjersti & Czado, Claudia & Frigessi, Arnoldo & Bakken, Henrik, 2009. "Pair-copula constructions of multiple dependence," Insurance: Mathematics and Economics, Elsevier, vol. 44(2), pages 182-198, April.
    2. Müller, Alfred & Scarsini, Marco, 2005. "Archimedean copulæ and positive dependence," Journal of Multivariate Analysis, Elsevier, vol. 93(2), pages 434-445, April.
    3. Fantazzini, Dean, 2009. "The effects of misspecified marginals and copulas on computing the value at risk: A Monte Carlo study," Computational Statistics & Data Analysis, Elsevier, vol. 53(6), pages 2168-2188, April.
    4. Cornelia Savu & Mark Trede, 2010. "Hierarchies of Archimedean copulas," Quantitative Finance, Taylor & Francis Journals, vol. 10(3), pages 295-304.
    5. François Longin, 2001. "Extreme Correlation of International Equity Markets," Journal of Finance, American Finance Association, vol. 56(2), pages 649-676, April.
    6. 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.
    7. W. Breymann & A. Dias & P. Embrechts, 2003. "Dependence structures for multivariate high-frequency data in finance," Quantitative Finance, Taylor & Francis Journals, vol. 3(1), pages 1-14.
    8. Jean-David FERMANIAN & Olivier SCAILLET, 2003. "Nonparametric Estimation of Copulas for Time Series," FAME Research Paper Series rp57, International Center for Financial Asset Management and Engineering.
    9. Niall Whelan, 2004. "Sampling from Archimedean copulas," Quantitative Finance, Taylor & Francis Journals, vol. 4(3), pages 339-352.
    10. Jondeau, Eric & Rockinger, Michael, 2003. "Conditional volatility, skewness, and kurtosis: existence, persistence, and comovements," Journal of Economic Dynamics and Control, Elsevier, vol. 27(10), pages 1699-1737, August.
    11. Bouye, Eric & Durlleman, Valdo & Nikeghbali, Ashkan & Riboulet, Gaël & Roncalli, Thierry, 2000. "Copulas for finance," MPRA Paper 37359, University Library of Munich, Germany.
    12. Andrew J. Patton, 2006. "Modelling Asymmetric Exchange Rate Dependence," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 47(2), pages 527-556, May.
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    Cited by:

    1. Travkin, A., 2015. "Estimating Pair-Copula Constructions Using Empirical Tail Dependence Functions: an Application to Russian Stock Market," Journal of the New Economic Association, New Economic Association, vol. 25(1), pages 39-55.
    2. Blagoveschensky, Yury, 2012. "Basics of copula’s theory," Applied Econometrics, Publishing House "SINERGIA PRESS", vol. 26(2), pages 113-130.
    3. Travkin, Alexandr, 2013. "Pair copula constructions in portfolio optimization ploblem," Applied Econometrics, Publishing House "SINERGIA PRESS", vol. 32(4), pages 110-133.
    4. Balaev, Alexey, 2014. "The copula based on multivariate t-distribution with vector of degrees of freedom," Applied Econometrics, Publishing House "SINERGIA PRESS", vol. 33(1), pages 90-110.
    5. Knyazev, Alexander & Lepekhin, Oleg & Shemyakin, Arkady, 2016. "Joint distribution of stock indices: Methodological aspects of construction and selection of copula models," Applied Econometrics, Publishing House "SINERGIA PRESS", vol. 42, pages 30-53.
    6. Penikas, Henry, 2014. "Investment portfolio risk modelling based on hierarchical copulas," Applied Econometrics, Publishing House "SINERGIA PRESS", vol. 35(3), pages 18-38.
    7. Fantazzini, Dean, 2011. "Analysis of multidimensional probability distributions with copula functions. II," Applied Econometrics, Publishing House "SINERGIA PRESS", vol. 23(3), pages 98-132.
    8. repec:nea:journl:y:2017:i:35:p:33-52 is not listed on IDEAS
    9. Fantazzini, Dean, 2011. "Analysis of multidimensional probability distributions with copula functions. III," Applied Econometrics, Publishing House "SINERGIA PRESS", vol. 24(4), pages 100-130.

    More about this item

    Keywords

    copula; multivariate distribution; elliptical copulas; Archimedean copula; hierarchical copula;

    JEL classification:

    • C49 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Other
    • C69 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Other

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