IDEAS home Printed from https://ideas.repec.org/a/ris/apltrx/0077.html
   My bibliography  Save this article

Analysis of multidimensional probability distributions with copula functions

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://pe.cemi.rssi.ru/pe_2011_2_98-134.pdf
    File Function: Full text
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Mohamed N. Jouini & Robert T. Clemen, 1996. "Copula Models for Aggregating Expert Opinions," Operations Research, INFORMS, vol. 44(3), pages 444-457, June.
    2. White,Halbert, 1996. "Estimation, Inference and Specification Analysis," Cambridge Books, Cambridge University Press, number 9780521574464.
    3. 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.
    4. Andrew J. Patton, 2004. "On the Out-of-Sample Importance of Skewness and Asymmetric Dependence for Asset Allocation," Journal of Financial Econometrics, Oxford University Press, vol. 2(1), pages 130-168.
    5. Gunky Kim & Mervyn J. Silvapulle & Paramsothy Silvapulle, 2007. "Estimating the Error Distribution in the Multivariate Heteroscedastic Time Series Models," Monash Econometrics and Business Statistics Working Papers 8/07, Monash University, Department of Econometrics and Business Statistics.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    10. 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.
    11. 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.
    12. Gourieroux,Christian & Monfort,Alain, 1995. "Statistics and Econometric Models," Cambridge Books, Cambridge University Press, number 9780521405515.
    13. Kim, Gunky & Silvapulle, Mervyn J. & Silvapulle, Paramsothy, 2007. "Comparison of semiparametric and parametric methods for estimating copulas," Computational Statistics & Data Analysis, Elsevier, vol. 51(6), pages 2836-2850, March.
    14. Ser-Huang Poon, 2004. "Extreme Value Dependence in Financial Markets: Diagnostics, Models, and Financial Implications," The Review of Financial Studies, Society for Financial Studies, vol. 17(2), pages 581-610.
    15. Yan, Jun, 2007. "Enjoy the Joy of Copulas: With a Package copula," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 21(i04).
    16. Cornelia Savu & Mark Trede, 2010. "Hierarchies of Archimedean copulas," Quantitative Finance, Taylor & Francis Journals, vol. 10(3), pages 295-304.
    17. Ruud, Paul A., 2000. "An Introduction to Classical Econometric Theory," OUP Catalogue, Oxford University Press, number 9780195111644.
    18. Marc Hallin & Thomas S. Ferguson & Christian Genest, 2000. "Kendall's tau for serial dependence," ULB Institutional Repository 2013/2093, ULB -- Universite Libre de Bruxelles.
    19. Müller, Alfred & Scarsini, Marco, 2005. "Archimedean copulæ and positive dependence," Journal of Multivariate Analysis, Elsevier, vol. 93(2), pages 434-445, April.
    20. 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.
    21. 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.
    22. François Longin & Bruno Solnik, 2001. "Extreme Correlation of International Equity Markets," Journal of Finance, American Finance Association, vol. 56(2), pages 649-676, April.
    23. 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.
    24. Chen, Xiaohong & Fan, Yanqin, 2006. "Estimation and model selection of semiparametric copula-based multivariate dynamic models under copula misspecification," Journal of Econometrics, Elsevier, vol. 135(1-2), pages 125-154.
    25. Niall Whelan, 2004. "Sampling from Archimedean copulas," Quantitative Finance, Taylor & Francis Journals, vol. 4(3), pages 339-352.
    26. Yannick Malevergne & Didier Sornette, 2006. "Extreme Financial Risks : From Dependence to Risk Management," Post-Print hal-02298069, HAL.
    27. Bouye, Eric & Durlleman, Valdo & Nikeghbali, Ashkan & Riboulet, Gaël & Roncalli, Thierry, 2000. "Copulas for finance," MPRA Paper 37359, University Library of Munich, Germany.
    28. Rafael Schmidt, 2002. "Tail dependence for elliptically contoured distributions," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 55(2), pages 301-327, May.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Patton, Andrew J., 2012. "A review of copula models for economic time series," Journal of Multivariate Analysis, Elsevier, vol. 110(C), pages 4-18.
    2. Patton, Andrew, 2013. "Copula Methods for Forecasting Multivariate Time Series," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 2, chapter 0, pages 899-960, Elsevier.
    3. Roch, Oriol & Alegre, Antonio, 2006. "Testing the bivariate distribution of daily equity returns using copulas. An application to the Spanish stock market," Computational Statistics & Data Analysis, Elsevier, vol. 51(2), pages 1312-1329, November.
    4. Fengler, Matthias & Okhrin, Ostap, 2012. "Realized Copula," Economics Working Paper Series 1214, University of St. Gallen, School of Economics and Political Science.
    5. Gregor Weiß, 2013. "Copula-GARCH versus dynamic conditional correlation: an empirical study on VaR and ES forecasting accuracy," Review of Quantitative Finance and Accounting, Springer, vol. 41(2), pages 179-202, August.
    6. Siburg, Karl Friedrich & Stoimenov, Pavel & Weiß, Gregor N.F., 2015. "Forecasting portfolio-Value-at-Risk with nonparametric lower tail dependence estimates," Journal of Banking & Finance, Elsevier, vol. 54(C), pages 129-140.
    7. Okhrin, Ostap & Okhrin, Yarema & Schmid, Wolfgang, 2013. "On the structure and estimation of hierarchical Archimedean copulas," Journal of Econometrics, Elsevier, vol. 173(2), pages 189-204.
    8. Duy Duong & Toan Luu Duc Huynh, 2020. "Tail dependence in emerging ASEAN-6 equity markets: empirical evidence from quantitative approaches," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 6(1), pages 1-26, December.
    9. Zhu, Wenjun & Wang, Chou-Wen & Tan, Ken Seng, 2016. "Structure and estimation of Lévy subordinated hierarchical Archimedean copulas (LSHAC): Theory and empirical tests," Journal of Banking & Finance, Elsevier, vol. 69(C), pages 20-36.
    10. Ostap Okhrin, 2010. "Fitting high-dimensional Copulae to Data," SFB 649 Discussion Papers SFB649DP2010-022, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    11. 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.
    12. Fengler, Matthias R. & Okhrin, Ostap, 2016. "Managing risk with a realized copula parameter," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 131-152.
    13. Chollete, Loran & Ning, Cathy, 2010. "Asymmetric Dependence in US Financial Risk Factors?," UiS Working Papers in Economics and Finance 2011/2, University of Stavanger.
    14. Agbeyegbe, Terence D., 2015. "An inverted U-shaped crude oil price return-implied volatility relationship," Review of Financial Economics, Elsevier, vol. 27(C), pages 28-45.
    15. 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.
    16. Reboredo, Juan C., 2012. "Do food and oil prices co-move?," Energy Policy, Elsevier, vol. 49(C), pages 456-467.
    17. Oriol Roch Casellas & Antonio Alegre Escolano, 2005. "Testing the bivariate distribution of daily equity returns using copulas. An application to the Spanish stock market," Working Papers in Economics 143, Universitat de Barcelona. Espai de Recerca en Economia.
    18. Weiß, Gregor N.F. & Scheffer, Marcus, 2015. "Mixture pair-copula-constructions," Journal of Banking & Finance, Elsevier, vol. 54(C), pages 175-191.
    19. Grundke, Peter & Polle, Simone, 2012. "Crisis and risk dependencies," European Journal of Operational Research, Elsevier, vol. 223(2), pages 518-528.
    20. Christoffersen, Peter & Langlois, Hugues, 2013. "The Joint Dynamics of Equity Market Factors," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 48(5), pages 1371-1404, October.

    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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:ris:apltrx:0077. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Anatoly Peresetsky (email available below). General contact details of provider: http://appliedeconometrics.cemi.rssi.ru/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.