IDEAS home Printed from https://ideas.repec.org/a/bla/scjsta/v41y2014i2p436-459.html
   My bibliography  Save this article

The Copula Information Criteria

Author

Listed:
  • Steffen Grønneberg
  • Nils Lid Hjort

Abstract

type="main" xml:id="sjos12042-abs-0001"> We derive two types of Akaike information criterion (AIC)-like model-selection formulae for the semiparametric pseudo-maximum likelihood procedure. We first adapt the arguments leading to the original AIC formula, related to empirical estimation of a certain Kullback–Leibler information distance. This gives a significantly different formula compared with the AIC, which we name the copula information criterion. However, we show that such a model-selection procedure cannot exist for copula models with densities that grow very fast near the edge of the unit cube. This problem affects most popular copula models. We then derive what we call the cross-validation copula information criterion, which exists under weak conditions and is a first-order approximation to exact cross validation. This formula is very similar to the standard AIC formula but has slightly different motivation. A brief illustration with real data is given.

Suggested Citation

  • Steffen Grønneberg & Nils Lid Hjort, 2014. "The Copula Information Criteria," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 41(2), pages 436-459, June.
    • Handle: RePEc:bla:scjsta:v:41:y:2014:i:2:p:436-459
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1111/sjos.12042
    Download Restriction: Access to full text is restricted to subscribers.
    ---><---

    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. Christian Genest & Jean‐François Quessy & Bruno Rémillard, 2006. "Goodness‐of‐fit Procedures for Copula Models Based on the Probability Integral Transformation," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 33(2), pages 337-366, June.
    2. Panchenko, Valentyn, 2005. "Goodness-of-fit test for copulas," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 355(1), pages 176-182.
    3. Claeskens,Gerda & Hjort,Nils Lid, 2008. "Model Selection and Model Averaging," Cambridge Books, Cambridge University Press, number 9780521852258, January.
    4. Segers, Johan, 2012. "Asymptotics of empirical copula processes under non-restrictive smoothness assumptions," LIDAM Reprints ISBA 2012009, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    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. Suneerat Srisopa & Peerapong Luamka & Saowanee Rattanawan & Khanitta Somtrakoon & Piyapatr Busababodhin, 2023. "Analyzing Spatial Dependence of Rice Production in Northeast Thailand for Sustainable Agriculture: An Optimal Copula Function Approach," Sustainability, MDPI, vol. 15(20), pages 1-21, October.
    2. Bolancé, Catalina & Bahraoui, Zuhair & Artís, Manuel, 2014. "Quantifying the risk using copulae with nonparametric marginals," Insurance: Mathematics and Economics, Elsevier, vol. 58(C), pages 46-56.
    3. Keay, Myoung-Jin, 2016. "Partial copula methods for models with multiple discrete endogenous explanatory variables and sample selection," Economics Letters, Elsevier, vol. 144(C), pages 85-87.
    4. Sehee Kim & Yi Li & Donna Spiegelman, 2016. "A semiparametric copula method for Cox models with covariate measurement error," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 22(1), pages 1-16, January.
    5. Candida Geerdens & Gerda Claeskens & Paul Janssen, 2016. "Copula based flexible modeling of associations between clustered event times," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 22(3), pages 363-381, July.
    6. Elisa Perrone & Andreas Rappold & Werner G. Müller, 2017. "$$D_s$$ D s -optimality in copula models," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 26(3), pages 403-418, August.
    7. Einolander, Johannes & Lahdelma, Risto, 2022. "Multivariate copula procedure for electric vehicle charging event simulation," Energy, Elsevier, vol. 238(PA).
    8. Ahmet Akca & Ethem Çanakoğlu, 2021. "Adaptive stochastic risk estimation of firm operating profit," Economia e Politica Industriale: Journal of Industrial and Business Economics, Springer;Associazione Amici di Economia e Politica Industriale, vol. 48(3), pages 463-504, September.
    9. Nurulkamal Masseran, 2021. "Modeling the Characteristics of Unhealthy Air Pollution Events: A Copula Approach," IJERPH, MDPI, vol. 18(16), pages 1-18, August.
    10. Catalina Bolancé & Montserrat Guillén & Alemar Padilla, 2015. "Estimación del riesgo mediante el ajuste de cópulas," Working Papers 2015-01, Universitat de Barcelona, UB Riskcenter.
    11. Ko, Vinnie & Hjort, Nils Lid, 2019. "Copula information criterion for model selection with two-stage maximum likelihood estimation," Econometrics and Statistics, Elsevier, vol. 12(C), pages 167-180.
    12. Calabrese, Raffaella & Osmetti, Silvia Angela, 2019. "A new approach to measure systemic risk: A bivariate copula model for dependent censored data," European Journal of Operational Research, Elsevier, vol. 279(3), pages 1053-1064.
    13. Mazo, Gildas & Averyanov, Yaroslav, 2019. "Constraining kernel estimators in semiparametric copula mixture models," Computational Statistics & Data Analysis, Elsevier, vol. 138(C), pages 170-189.
    14. Tepegjozova Marija & Zhou Jing & Claeskens Gerda & Czado Claudia, 2022. "Nonparametric C- and D-vine-based quantile regression," Dependence Modeling, De Gruyter, vol. 10(1), pages 1-21, January.
    15. Ko, Vinnie & Hjort, Nils Lid, 2019. "Model robust inference with two-stage maximum likelihood estimation for copulas," Journal of Multivariate Analysis, Elsevier, vol. 171(C), pages 362-381.
    16. F. Marta L. Di Lascio & Andrea Menapace & Maurizio Righetti, 2020. "Joint and conditional dependence modelling of peak district heating demand and outdoor temperature: a copula-based approach," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 29(2), pages 373-395, June.
    17. Fontaine, Charles & Frostig, Ron D. & Ombao, Hernando, 2020. "Modeling non-linear spectral domain dependence using copulas with applications to rat local field potentials," Econometrics and Statistics, Elsevier, vol. 15(C), pages 85-103.

    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. Jean-David Fermanian, 2012. "An overview of the goodness-of-fit test problem for copulas," Papers 1211.4416, arXiv.org.
    2. Marc Gronwald & Janina Ketterer & Stefan Trück, 2011. "The Dependence Structure between Carbon Emission Allowances and Financial Markets - A Copula Analysis," CESifo Working Paper Series 3418, CESifo.
    3. Can, S.U. & Einmahl, John & Laeven, R.J.A., 2020. "Goodness-of-fit testing for copulas: A distribution-free approach," Other publications TiSEM 211b2be9-b46e-41e2-9b95-1, Tilburg University, School of Economics and Management.
    4. Diks, Cees & Panchenko, Valentyn & van Dijk, Dick, 2010. "Out-of-sample comparison of copula specifications in multivariate density forecasts," Journal of Economic Dynamics and Control, Elsevier, vol. 34(9), pages 1596-1609, September.
    5. Can, S.U. & Einmahl, John & Laeven, R.J.A., 2017. "Asymptotically Distribution-Free Goodness-of-Fit Testing for Copulas," Discussion Paper 2017-052, Tilburg University, Center for Economic Research.
    6. Jäschke, Stefan, 2014. "Estimation of risk measures in energy portfolios using modern copula techniques," Computational Statistics & Data Analysis, Elsevier, vol. 76(C), pages 359-376.
    7. Quessy, Jean-François & Bahraoui, Tarik, 2014. "Weak convergence of empirical and bootstrapped C-power processes and application to copula goodness-of-fit," Journal of Multivariate Analysis, Elsevier, vol. 129(C), pages 16-36.
    8. Bruno Rémillard, 2017. "Goodness-of-Fit Tests for Copulas of Multivariate Time Series," Econometrics, MDPI, vol. 5(1), pages 1-23, March.
    9. Yiran Chen & Giray Ökten, 2022. "A goodness-of-fit test for copulas based on the collision test," Statistical Papers, Springer, vol. 63(5), pages 1369-1385, October.
    10. 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.
    11. Stefan Mittnik & Sandra Paterlini & Tina Yener, 2011. "Operational–risk Dependencies and the Determination of Risk Capital," Center for Economic Research (RECent) 070, University of Modena and Reggio E., Dept. of Economics "Marco Biagi".
    12. Kitagawa, Toru & Muris, Chris, 2016. "Model averaging in semiparametric estimation of treatment effects," Journal of Econometrics, Elsevier, vol. 193(1), pages 271-289.
    13. Jeffrey S. Racine & Qi Li & Dalei Yu & Li Zheng, 2023. "Optimal Model Averaging of Mixed-Data Kernel-Weighted Spline Regressions," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 41(4), pages 1251-1261, October.
    14. Philippe Goulet Coulombe & Maxime Leroux & Dalibor Stevanovic & Stéphane Surprenant, 2022. "How is machine learning useful for macroeconomic forecasting?," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 37(5), pages 920-964, August.
    15. Davide Fiaschi & Andrea Mario Lavezzi & Angela Parenti, 2020. "Deep and Proximate Determinants of the World Income Distribution," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 66(3), pages 677-710, September.
    16. Beare, Brendan K. & Seo, Juwon, 2020. "Randomization Tests Of Copula Symmetry," Econometric Theory, Cambridge University Press, vol. 36(6), pages 1025-1063, December.
    17. 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.
    18. Fabio Canova & Christian Matthes, 2021. "Dealing with misspecification in structural macroeconometric models," Quantitative Economics, Econometric Society, vol. 12(2), pages 313-350, May.
    19. Yu, Jun & Meng, Xiran & Wang, Yaping, 2023. "Optimal designs for semi-parametric dose-response models under random contamination," Computational Statistics & Data Analysis, Elsevier, vol. 178(C).
    20. Mainik, Georg, 2015. "Risk aggregation with empirical margins: Latin hypercubes, empirical copulas, and convergence of sum distributions," Journal of Multivariate Analysis, Elsevier, vol. 141(C), pages 197-216.

    More about this item

    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:bla:scjsta:v:41:y:2014:i:2:p:436-459. 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: Wiley Content Delivery (email available below). General contact details of provider: http://www.blackwellpublishing.com/journal.asp?ref=0303-6898 .

    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.