IDEAS home Printed from https://ideas.repec.org/a/wsi/ijitdm/v18y2019i01ns021962201750047x.html
   My bibliography  Save this article

Multivariate Skew Normal Copula for Asymmetric Dependence: Estimation and Application

Author

Listed:
  • Zheng Wei

    (Department of Mathematics and Statistics, University of Maine, Orono, Maine, 04469-5752, USA)

  • Seongyong Kim

    (Department of Applied Statistics, Hoseo University, Asan-si, Chungcheongnam-do, 31499, Republic of Korea)

  • Boseung Choi

    (Korea University Sejong Campus, Division of Economics and Statistics, Department of National Statistics, Sejong, 30019, Republic of Korea)

  • Daeyoung Kim

    (Department of Mathematics and Statistics, University of Massachusetts, Amherst, Massachusetts, 01003-9305, USA)

Abstract

The exchangeability and radial symmetry assumptions on the dependence structure of the multivariate data are restrictive in practical situations where the variables of interest are not likely to be associated to each other in an identical manner. In this paper, we propose a flexible class of multivariate skew normal copulas to model high-dimensional asymmetric dependence patterns. The proposed copulas have two sets of parameters capturing asymmetric dependence, one for association between the variables and the other for skewness of the variables. In order to efficiently estimate the two sets of parameters, we introduce the block coordinate ascent algorithm and discuss its convergence property. The proposed class of multivariate skew normal copulas is illustrated using a real data set.

Suggested Citation

  • Zheng Wei & Seongyong Kim & Boseung Choi & Daeyoung Kim, 2019. "Multivariate Skew Normal Copula for Asymmetric Dependence: Estimation and Application," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 18(01), pages 365-387, January.
    • Handle: RePEc:wsi:ijitdm:v:18:y:2019:i:01:n:s021962201750047x
    DOI: 10.1142/S021962201750047X
    as

    Download full text from publisher

    File URL: http://www.worldscientific.com/doi/abs/10.1142/S021962201750047X
    Download Restriction: Access to full text is restricted to subscribers
    File URL: https://libkey.io/10.1142/S021962201750047X?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. François Longin & Bruno Solnik, 2001. "Extreme Correlation of International Equity Markets," Journal of Finance, American Finance Association, vol. 56(2), pages 649-676, April.
    2. Alexander J. McNeil & Rüdiger Frey & Paul Embrechts, 2015. "Quantitative Risk Management: Concepts, Techniques and Tools Revised edition," Economics Books, Princeton University Press, edition 2, number 10496.
    3. Acar, Elif F. & Genest, Christian & Nešlehová, Johanna, 2012. "Beyond simplified pair-copula constructions," Journal of Multivariate Analysis, Elsevier, vol. 110(C), pages 74-90.
    4. Edward Frees & Emiliano Valdez, 1998. "Understanding Relationships Using Copulas," North American Actuarial Journal, Taylor & Francis Journals, vol. 2(1), pages 1-25.
    5. Krupskii, Pavel & Joe, Harry, 2015. "Structured factor copula models: Theory, inference and computation," Journal of Multivariate Analysis, Elsevier, vol. 138(C), pages 53-73.
    6. Gang Kou & Yanqun Lu & Yi Peng & Yong Shi, 2012. "Evaluation Of Classification Algorithms Using Mcdm And Rank Correlation," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 11(01), pages 197-225.
    7. Schepsmeier, Ulf, 2015. "Efficient information based goodness-of-fit tests for vine copula models with fixed margins: A comprehensive review," Journal of Multivariate Analysis, Elsevier, vol. 138(C), pages 34-52.
    8. Liebscher, Eckhard, 2008. "Construction of asymmetric multivariate copulas," Journal of Multivariate Analysis, Elsevier, vol. 99(10), pages 2234-2250, November.
    9. Wang, Tonghui & Li, Baokun & Gupta, Arjun K., 2009. "Distribution of quadratic forms under skew normal settings," Journal of Multivariate Analysis, Elsevier, vol. 100(3), pages 533-545, March.
    10. A. Azzalini & A. Capitanio, 1999. "Statistical applications of the multivariate skew normal distribution," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(3), pages 579-602.
    11. 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.
    12. McNeil, Alexander J. & Neslehová, Johanna, 2010. "From Archimedean to Liouville copulas," Journal of Multivariate Analysis, Elsevier, vol. 101(8), pages 1772-1790, September.
    13. Stöber, Jakob & Joe, Harry & Czado, Claudia, 2013. "Simplified pair copula constructions—Limitations and extensions," Journal of Multivariate Analysis, Elsevier, vol. 119(C), pages 101-118.
    14. 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.
    15. Krupskii, Pavel & Joe, Harry, 2013. "Factor copula models for multivariate data," Journal of Multivariate Analysis, Elsevier, vol. 120(C), pages 85-101.
    16. Avanzi, Benjamin & Tao, Jamie & Wong, Bernard & Yang, Xinda, 2016. "Capturing non-exchangeable dependence in multivariate loss processes with nested Archimedean Lévy copulas," Annals of Actuarial Science, Cambridge University Press, vol. 10(1), pages 87-117, March.
    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. Kexin Li & Jianxu Liu & Yuting Xue & Sanzidur Rahman & Songsak Sriboonchitta, 2022. "Consequences of Ignoring Dependent Error Components and Heterogeneity in a Stochastic Frontier Model: An Application to Rice Producers in Northern Thailand," Agriculture, MDPI, vol. 12(8), pages 1-17, July.
    2. Teena Goyal & Piyush K. Rai & Sandeep K. Maurya, 2020. "Bayesian Estimation for GDUS Exponential Distribution Under Type-I Progressive Hybrid Censoring," Annals of Data Science, Springer, vol. 7(2), pages 307-345, June.
    3. Jianxu Liu & Quanrui Song & Yang Qi & Sanzidur Rahman & Songsak Sriboonchitta, 2020. "Measurement of Systemic Risk in Global Financial Markets and Its Application in Forecasting Trading Decisions," Sustainability, MDPI, vol. 12(10), pages 1-15, May.
    4. Jianxu Liu & Mengjiao Wang & Ji Ma & Sanzidur Rahman & Songsak Sriboonchitta, 2020. "A Simultaneous Stochastic Frontier Model with Dependent Error Components and Dependent Composite Errors: An Application to Chinese Banking Industry," Mathematics, MDPI, vol. 8(2), pages 1-23, February.
    5. David A. Alilah & C. O. Ouma & E. O. Ombaka, 2023. "Efficiency of Domain Mean Estimators in the Presence of Non-response Using Two-Stage Sampling with Non-linear and Linear Cost Function," Annals of Data Science, Springer, vol. 10(2), pages 291-316, April.
    6. Jianxu Liu & Mengjiao Wang & Songsak Sriboonchitta, 2019. "Examining the Interdependence between the Exchange Rates of China and ASEAN Countries: A Canonical Vine Copula Approach," Sustainability, MDPI, vol. 11(19), pages 1-20, October.

    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. Tachibana, Minoru, 2022. "Safe haven assets for international stock markets: A regime-switching factor copula approach," Research in International Business and Finance, Elsevier, vol. 60(C).
    2. Kajal Lahiri & Liu Yang, 2023. "Predicting binary outcomes based on the pair-copula construction," Empirical Economics, Springer, vol. 64(6), pages 3089-3119, June.
    3. Minoru Tachibana, 2020. "Flight-to-quality in the stock–bond return relation: a regime-switching copula approach," Financial Markets and Portfolio Management, Springer;Swiss Society for Financial Market Research, vol. 34(4), pages 429-470, December.
    4. BenSaïda, Ahmed, 2018. "The contagion effect in European sovereign debt markets: A regime-switching vine copula approach," International Review of Financial Analysis, Elsevier, vol. 58(C), pages 153-165.
    5. Hua, Lei & Joe, Harry, 2017. "Multivariate dependence modeling based on comonotonic factors," Journal of Multivariate Analysis, Elsevier, vol. 155(C), pages 317-333.
    6. Michael Stanley Smith, 2021. "Implicit Copulas: An Overview," Papers 2109.04718, arXiv.org.
    7. Perreault, Samuel & Duchesne, Thierry & Nešlehová, Johanna G., 2019. "Detection of block-exchangeable structure in large-scale correlation matrices," Journal of Multivariate Analysis, Elsevier, vol. 169(C), pages 400-422.
    8. Portier, François & Segers, Johan, 2018. "On the weak convergence of the empirical conditional copula under a simplifying assumption," Journal of Multivariate Analysis, Elsevier, vol. 166(C), pages 160-181.
    9. Christian Genest & Johanna Nešlehová & Johanna Ziegel, 2011. "Inference in multivariate Archimedean copula models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 20(2), pages 223-256, August.
    10. Stöber, Jakob & Joe, Harry & Czado, Claudia, 2013. "Simplified pair copula constructions—Limitations and extensions," Journal of Multivariate Analysis, Elsevier, vol. 119(C), pages 101-118.
    11. Azam, Kazim, 2014. "Dependence Analysis between Foreign Exchange Rates: A Semi-Parametric Copula Approach," Economic Research Papers 270231, University of Warwick - Department of Economics.
    12. 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.
    13. Derumigny Alexis & Fermanian Jean-David, 2017. "About tests of the “simplifying” assumption for conditional copulas," Dependence Modeling, De Gruyter, vol. 5(1), pages 154-197, August.
    14. 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.
    15. Manner, Hans & Stark, Florian & Wied, Dominik, 2019. "Testing for structural breaks in factor copula models," Journal of Econometrics, Elsevier, vol. 208(2), pages 324-345.
    16. Chaoubi, Ihsan & Cossette, Hélène & Marceau, Etienne & Robert, Christian Y., 2021. "Hierarchical copulas with Archimedean blocks and asymmetric between-block pairs," Computational Statistics & Data Analysis, Elsevier, vol. 154(C).
    17. Dong Hwan Oh & Andrew J. Patton, 2017. "Modeling Dependence in High Dimensions With Factor Copulas," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 35(1), pages 139-154, January.
    18. Hua, Lei, 2017. "On a bivariate copula with both upper and lower full-range tail dependence," Insurance: Mathematics and Economics, Elsevier, vol. 73(C), pages 94-104.
    19. Christian Genest & Johanna Nešlehová & Jean-François Quessy, 2012. "Tests of symmetry for bivariate copulas," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 64(4), pages 811-834, August.
    20. Anne Opschoor & André Lucas & István Barra & Dick van Dijk, 2021. "Closed-Form Multi-Factor Copula Models With Observation-Driven Dynamic Factor Loadings," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 39(4), pages 1066-1079, October.

    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:wsi:ijitdm:v:18:y:2019:i:01:n:s021962201750047x. 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: Tai Tone Lim (email available below). General contact details of provider: http://www.worldscinet.com/ijitdm/ijitdm.shtml .

    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.