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Analysis of multidimensional probability distributions with copula functions

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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, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 22(2), pages 98-134.
    • Handle: RePEc:ris:apltrx:0077
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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. Penikas, Henry, 2014. "Investment portfolio risk modelling based on hierarchical copulas," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 35(3), pages 18-38.
    3. Blagoveschensky, Yury, 2012. "Basics of copula’s theory," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 26(2), pages 113-130.
    4. Travkin, Alexandr, 2013. "Pair copula constructions in portfolio optimization ploblem," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 32(4), pages 110-133.
    5. Balaev, Alexey, 2014. "The copula based on multivariate t-distribution with vector of degrees of freedom," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 33(1), pages 90-110.
    6. Knyazev, Alexander & Lepekhin, Oleg & Shemyakin, Arkady, 2016. "Joint distribution of stock indices: Methodological aspects of construction and selection of copula models," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 42, pages 30-53.
    7. Fantazzini, Dean, 2011. "Analysis of multidimensional probability distributions with copula functions. II," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 23(3), pages 98-132.
    8. Kalyagin, V. & Koldanov, A. & Koldanov, P. & Pardalos, P., 2017. "Statistical Procedures for Stock Markets Network Structures Identification," Journal of the New Economic Association, New Economic Association, vol. 35(3), pages 33-52.
    9. Fantazzini, Dean, 2011. "Analysis of multidimensional probability distributions with copula functions. III," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 24(4), pages 100-130.

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    More about this item

    Keywords

    copula; multivariate distribution; elliptical copulas; Archimedean copula; hierarchical copula;
    All these keywords.

    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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