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Archimedean Copulas and Temporal Dependence

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  • Beare, Brendan K.
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    Abstract

    We study the dependence properties of stationary Markov chains generated by Archimedean copulas. Under some simple regularity conditions, we show that regular variation of the Archimedean generator at zero and one implies geometric orgodicityof the associated Markov chain. We verify our assumptions for a range of Archimedean copulas used in applications.

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    File URL: http://www.escholarship.org/uc/item/0xh8q1g3.pdf;origin=repeccitec
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    Bibliographic Info

    Paper provided by Department of Economics, UC San Diego in its series University of California at San Diego, Economics Working Paper Series with number qt0xh8q1g3.

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    Date of creation: 09 Sep 2010
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    Handle: RePEc:cdl:ucsdec:qt0xh8q1g3

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    Keywords: archimedean copula; geometric ergodicity; Markov chain; mixing; regular variation; tail dependence; Social and Behavioral Sciences;

    References

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    1. Charpentier, Arthur & Segers, Johan, 2007. "Lower tail dependence for Archimedean copulas: Characterizations and pitfalls," Insurance: Mathematics and Economics, Elsevier, vol. 40(3), pages 525-532, May.
    2. Chen, Xiaohong & Fan, Yanqin, 2006. "Estimation of copula-based semiparametric time series models," Journal of Econometrics, Elsevier, vol. 130(2), pages 307-335, February.
    3. Patrick Gagliardini & Christian Gourieroux, 2002. "Duration Time Series Models with Proportional Hazard," Working Papers 2002-21, Centre de Recherche en Economie et Statistique.
    4. Ibragimov, Rustam, 2009. "Copula-Based Characterizations For Higher Order Markov Processes," Econometric Theory, Cambridge University Press, vol. 25(03), pages 819-846, June.
    5. Xiaohong Chen & Wei Biao Wu & Yanping Yi, 2009. "Efficient Estimation of Copula-based Semiparametric Markov Models," Cowles Foundation Discussion Papers 1691, Cowles Foundation for Research in Economics, Yale University, revised Mar 2009.
    6. Xiaohong Chen & Roger Koenker & Zhijie Xiao, 2008. "Copula-based nonlinear quantile autoregression," CeMMAP working papers CWP27/08, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    7. Eric Bouye & Mark Salmon, 2009. "Dynamic copula quantile regressions and tail area dynamic dependence in Forex markets," The European Journal of Finance, Taylor & Francis Journals, vol. 15(7-8), pages 721-750.
    8. Juri, Alessandro & Wuthrich, Mario V., 2002. "Copula convergence theorems for tail events," Insurance: Mathematics and Economics, Elsevier, vol. 30(3), pages 405-420, June.
    9. repec:sae:ecolab:v:16:y:2006:i:2:p:1-2 is not listed on IDEAS
    10. Brendan K. Beare, 2010. "Copulas and Temporal Dependence," Econometrica, Econometric Society, vol. 78(1), pages 395-410, 01.
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    Cited by:
    1. Beare, Brendan K. & Seo, Juwon, 2012. "Time irreversible copula-based Markov Models," University of California at San Diego, Economics Working Paper Series qt31f8500p, Department of Economics, UC San Diego.
    2. Berghaus, Betina & Bücher, Axel, 2014. "Nonparametric tests for tail monotonicity," Journal of Econometrics, Elsevier, vol. 180(2), pages 117-126.
    3. Righi, Marcelo Brutti & Ceretta, Paulo Sergio, 2013. "Estimating non-linear serial and cross-interdependence between financial assets," Journal of Banking & Finance, Elsevier, vol. 37(3), pages 837-846.
    4. Oleg Sokolinskiy & Dick van Dijk, 2011. "Forecasting Volatility with Copula-Based Time Series Models," Tinbergen Institute Discussion Papers 11-125/4, Tinbergen Institute.
    5. Cherubini, Umberto & Mulinacci, Sabrina & Romagnoli, Silvia, 2011. "A copula-based model of speculative price dynamics in discrete time," Journal of Multivariate Analysis, Elsevier, vol. 102(6), pages 1047-1063, July.
    6. Sebastian Kiwitt & Natalie Neumeyer, 2013. "A note on testing independence by a copula-based order selection approach," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer, vol. 22(1), pages 62-82, March.
    7. Elena Di Bernardino & Didier Rullière, 2014. "On tail dependence coefficients of transformed multivariate Archimedean copulas," Working Papers hal-00992707, HAL.
    8. Beatriz Vaz de Melo Mendes & Cecília Aíube, 2011. "Copula based models for serial dependence," International Journal of Managerial Finance, Emerald Group Publishing, vol. 7(1), pages 68-82, February.
    9. Margaret Meyer & Bruno Strulovici, 2013. "The Supermodular Stochastic Ordering," Discussion Papers 1563, Northwestern University, Center for Mathematical Studies in Economics and Management Science.

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